Errata 2 (Second printing)
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Many occurences of "Anshel" were mis-spelled: this should be "Anshel",
not "Anschel".
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[page] [line] [original] -> [corrected]
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page x line -4: Roots ---> Roots of Primes
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page xiv line: -17 than here ---> here than
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page xv line 7: possibly ---> possible
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page sv line -15: eveyone ---> everyone
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page xix line -15: occured ---> occurred
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page 5 line -12: arithemetic ---> arithmetic
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page 6 line -8: give ---> gives
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page 8 line 18: q'-q ---> q-q'
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page 8 line -8: q'-q ---> q-q'
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page 19 line -10: subset ---> subsets
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page 28 line 8: Aand B ---> A and B
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page 28 line 12: another another ---> another
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page 40 line 13: the the ---> the
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page 41 lines 15-16: some of the frequencies are messed up, should be:
E-11, B-9, J-9, C-7, X-7, G-6, L-4, N-2, S-3, T-3
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page 43 line -18: whatseover ---> whatsoever
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page 44 line 3: n-characer ---> n-character
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page 45 line -13: amgibuities ---> ambiguities
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page 54 line -2: with the other ---> from the other
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page 55 line 4: 3, n+3, 3, ... ---> 3, n+3, ...
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page 55 line 7: shuffle, (or maybe two) ---> shuffle (or maybe two),
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page 55 line 9: 1,2,..., 2n-1 ---> 1,2, ..., 2n-1, 2n
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page 59 line 16: (3m+1)th, ---> (3m+1)th, ...,
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page 59 line 17: m+2th, 2m+2th, 3m+2th ---> (m+2)th, (2m+2)th, (3m+2)th,
...,
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page 61 line 5: m|N and n|N ---> m and n divide N.
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page 68 line 11: 3 of the 6 ---> 2 of the 3
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page 68 line 15: a key ---> this key
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page 68 line 19: 35 ---> 39
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page 73 line -7: ciphertext only ---> ciphertext-only
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page 74 line 22: eight ---> eighth
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page 75 line 10: 0.067 ---> 0.064
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page 75 line -10: 0--25 ---> 0-25
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page 75 line -7: P(y)=py0 py1 ... pyN-1
---> P(y)=(p liney0, py1, ..., pyN-1)
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page 75 line -7: P(y)=p'y0 p'y1 ... p'yN-1
---> P(y)=(p' liney0, p'y1, ..., p'yN-1)
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page 76 line 6: insert 1/N after = sign
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page 76 line 14: insert 1/N after = sign
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page 76 line 15: insert "So E(X)=E(Xi) for all i."
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page 77 line -3: 0.067 ---> 0.064
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page 79 line 10: 0.067 ---> 0.064
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page 79 bottom: Add: "95% of these are between 5% and 8%."
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page 81 line 3: Should screen for I>0.040, nor I>0.047
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page 82 line -17: y(3) = (y2,y3+m,y3+2m,...)
---> y(3) = (y3,y3+m,y3+2m,...)
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page 82 line -16: y(4) = (y3,y4+m,y4+2m,...)
---> y(4 line) = (y4,y4+m,y4+2m,...)
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page 81 line 1: shifting the slice by 3
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page 83 line -1: (k2 - k0) + (k1 - k0)
= (k2 line - k0) ---> (k2 line - k0)
- (k1 - k0) = (k2 line - k0)
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page 84 line -18: (k3 - k0) + (k1 - k0)
= (k3 line - k0) ---> (k3 line - k0)
- (k1 - k0) = (k3 line - k0)
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page 84 line -8: Add comment "Mildly surprising that correct shift has
index only 5.18%."
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page 85 line 4 and following: Should admit that we're now screening just
above 5.00%
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page 85 line 22: "all possibilities are excluded except TWO: k4-k0=16
and k4-k0=15 AND ALSO k4-k0=22
and k4-k0=21.
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page 90 5.1.02 [duplicates 22.1.07]
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page 90 5.1.03 [duplicates 5.1.02]
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page 93 line -7 : sigma2 = ---> sigma2<2 >=
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page 94 line -2: sqrt(p(1-p))/n ---> p(1-p)/epsilon2n
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page 98 line -5: while th eeach ---> while each
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page 99 line 21: Kerckhoff's ---> Kerckhoffs
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page 100 line 6: Kerckhoff's ---> Kerckhoffs
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page 100 line -10: eigth ---> eighth
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page 101 line 12: round is ---> round is a
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page 105 line 15: permutation ---> permutations
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page 109 line 8: A positive integer ---> An integer greater than 1
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page 109 line 14: A positive integer ---> An integer greater than 1
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page 109 line -10: equal n ---> equal to n
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page 110 line -1: (-y0) . n ---> (-qy0) . n
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page 113 line 1: integer ---> non-zero integer
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page 113 line 12: n = ---> N =
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page 113: n and N used interchangeably/inconsistently
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page 115: n and N used interchangeably/inconsistently
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page 116 line -21: other than 5 ---> not divisible by 5
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page 118 lines 10-12: Add "For 2m+1 to be prime requires that
m=2n for some n, but this is not a sufficient condition. No
Fermat prime is known beyond the case of 224+1."
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page 120 line 7: x > y ---> x and y such that |x| > |y|
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page 120 line 18: = y' - r' < r'-y'/2 = y'/2 ---> =< y' - r' <
y'-y'/2 = y'/2 [equality becomes less-or-equal]
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page 130 line 11: 18-3 ---> 3-18
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page 131 line -12: overline(10) ---> overline(9)
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page 133 line 9: is a ---> are
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page 133 line 10: 0 =< r < |m| and an integer q so that ---> integers
r and q with 0 =< r < |m| and
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page 135 7.7.15 three ---> four
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page 135 7.7.20 a=< ---> a0 [twice]
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page 136 line -17: m ---> n
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page 136 line -16: m ---> n
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page 136 line -15: m ---> n
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page 137 line 3: m ---> n
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pages 136-137 The m's and n's should be the same thing!
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page 137 7.8.04 2 is ---> 2 is not, but 3 is,
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page 138 7.8.12 logr2 = logrs . logs2
---> logr line2 = logrs . logs2 mod 16
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page 138 7.8.13 logrx = logrs . logsx
---> logr line2 = logrs . logs2 mod phi(m)
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page 143 and to end of section: "k" ---> "K"
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page 146 line 6: [missing equality sign between second and third matrices
in middle of equality]
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page 148 line -6: O(k) ---> O(h)
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page 148 line -6: O(hk) ---> O(h2)
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page 149 line 3: |f(x|) ---> |f(x)|
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page 150 line -12: equal ---> equal to
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page 152 line 7: (log102)l ---> (log102)-l
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page 154 line 17: to to ---> to
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page 154 line -9: 2log2N/2 ---> 2(log2N)/2
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page 157 line -5: s3, sN-1 ---> s3, ...,
sN-1
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page 157 line -3: sn-3 ---> sn-N+1
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page 158 line 4: s3, sN-1 ---> s3, ...,
sN-1
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page 161 line 23: m ---> p
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page 165 line 11: n ---> phi(n)
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page 165 line -10: -n(-phi(n)+1) ---> n-phi(n)+1
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page 166 line -5: there ---> the
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page 169 line -1: exponentiations ---> multiplications
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page 170 line 9: equal ---> equal to
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page 170 line 15: help: ---> help.
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page 170 line -14: occuring ---> occurringpage 175 line 20: add "These
special primes are Sophie Germain primes."
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page 178 line -16: bi ---> ci
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page 179 line -22: be be ---> be
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page 180 line 9: albk ---> aibj
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page 181 line 1: may may ---> may
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page 181 line 7: x ---> m
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page 181 line -2: h ---> m
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page 185 line -13: a2ba-1 ---> ab2a-1
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page 185 line -5: ei1 ---> ki1
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page 185 line -2: aiNei1 ---> ai1ki1
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page 185 line -1: ei1 ---> ki1
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page 187 line 13: effect ---> effects
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page 192 line -14: surely not ---> surely is not
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page 195 line 2: theta(2e) = 2e+1 ln 2 ---> theta(2e)
=< 2e+1 ln 2
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page 196 line 5: Stieljes ---> Stieltjes
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page 196 line 8: [inside integral] theta(x) ---> theta(t)
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page 196 line 9: theta(x)=O(x) ---> theta(t) = O(t)
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page 196 line 10: [inside integral] O(x) ---> O(t)
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page 197 line 15: G. Riemann ---> B. Riemann
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page 202 line 5: +1 ---> +1)
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page 205 line 15: 19.34 ---> 10.34
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page 205 line 19: 725, ---> 725.
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page 205 line -5: 19*58 ---> 19.58
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page 208 line -2: n ---> m
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page 213 line -2: the the ---> the
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page 216 line 2: f2 compose f1 ---> f1
compose f2
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page 216 line -6: solutions) as ---> solutions as)
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page 218 line 10: b2 ---> b3
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page 219 line -8: 17 ---> 17,
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page 219 line -8: 13 ---> 29
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page 220 line 10: [delete dot before rightmost "4"]
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page 221 line -1: 21y ---> 42y
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page 223 line 6: f' circ g . g ---> f' circ g . g'
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page 224 line 8: f'(xn)-1 ---> f'(xn)-1)
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page 224 line -16: f(xn).tp ---> -f(xn).tp
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page 226 line -1: 1/(1-x) ---> 1/(1-x) - 1
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page 227 line 1: 1/(1-x) ---> (1/(1-x) - 1)
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page 227 line 5: 1 = 107 ---> q = 107
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page 230 line 3: not ---> no
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page 230 line 14: mod n ---> mod n.
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page 231 line 2: a efficient ---> an efficient
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page 246 line 7: [second quadratic symbol a mod n should be b mod n]
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page 247 line -5: 319 ---> quadratic symbol 3 over 19
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page 250 line -10: [in exponent] (n2-1)8 ---> (n2-1)/8
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page 250 line -4: [missing '+' between two fractions with denominators
8]
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page 257 line -18: p ---> n
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page 257 line -16: p ---> n
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page 267 line -11: form ---> forms
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page 267 17.1.02 integer n ---> integer n,
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page 277 line 2: that that ---> that
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page 282 line -7: should define ni=(1/M) % mi
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page 282 line -4: Ni ---> ni
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page 283 in the Theorem hk ---> hk-1
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page 283 line 13: hk ---> hk-1
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page 283 line -13: ai ---> mi
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page 283 line -3: ai ---> mi
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page 301 line -13: x3+x2+x+1 ---> x2+x
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page 301 line -11: 0 + 0 + 1 + 1 ---> 0 + 0
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page 301 line -9: 1 + 1 + 1 + 1 ---> 1 + 1
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page 302 problem 19.3.06: a ---> 1
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page 302 line -9: = x-1 ---> = -x+1
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page 302 line -8: x-1 ---> -x+1
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page 303 line 2: [delete "at each step"]
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page 315 line -7: fg ---> (fg)'
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page 321 line 12: phi(d) ---> phi(d)
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page 336 line -17: occuring ---> occurring
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page 340 line -1: [first] sn ---> 1
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page 340 line -1: sn-1 ---> 1
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page 341 line 2: sn+k-1 ---> 1
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page 341 line 2: sn-1 ---> 1
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page 341 line 5: numbers ---> nonzero numbers
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page 343 line -6: if if ---> if
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page 345 line 10: [italicize left parenthesis by "Proof"]
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page 346 line 3: special, case ---> special case
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page 347 line -6: ['F' in FpN should be bold]
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page 347 line -5: ['F' in FpN should be bold]
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page 347 line -4: ['F' in FpN should be bold]
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page 351 line 1: it i ---> it is
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page 352 line 5: an polynomial ---> a polynomial
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page 353 line 7: x73 ---> x73
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page 356 line -10: is the image of an inverse ---> is the inverse of the
image
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page 358 22.1.10 [duplicates 22.1.07]
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page 359 22.1.14 [duplicates proof on page 356]
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page 360 line 10: that that ---> that
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page 361 line -14: (gk)q ---> (gk)-q
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page 362 line 10: alright ---> all right
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page 362 line -16: homorphism ---> homomorphism
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page 362 22.2.02 Z/13 ---> Z/13x
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page 362 22.2.04 g24 g28 ---> g24, g28
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page 363 line 10: g-1e=g0 ---> g-1, e=g0
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page 366 line -4: N|l m ---> N|lm [remove space]
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page 367 line -19: version ---> version of
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page 367 line -8: odd. Let ... Let ---> odd. Let
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page 368 lines 6, 9, 13, 13: b ---> y
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page 368 line 19: 235 ---> 253
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page 375 : delete proposition, proven earlier (p. 261)
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page 377 line -15: [second quadratic symbol should be y mod n]
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page 377 line -13: [second quadratic symbol should be y mod n]
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page 377 line -11: [second quadratic symbol should be y mod n]
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page 379 line -1: ordp = ---> ordpk = --->
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page 380 line 9: ordp = ---> ordpk = --->
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page 382 line -13: an-1 ---> gn-1
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page 382 line -10: al ---> gl
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page 392 line 1: equal ei ---> equal to ei
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page 392 line -2: equal B ---> equal to B
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page 392 line -1: equal B ---> equal to B
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page 393 second bullet: rewrite as "replace b by br, where r=pi
ell
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page 396 in exercises 1-4 delete words "factor base"
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page 398 line -15: k=1 ---> u=1
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page 406 line 7: N-1 ---> K
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page 406 line 9: difficult ---> difficult condition
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page 409 line -2: n ---> N
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page 410 line -3: division ---> divisions
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page 413 line -16: operations ---> operations,
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page 413 line -10: m ---> n
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page 414 line -9: Yet these ---> Yet
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page 415 line 4: b mod n, ---> b mod n;
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page 415 line -4: ai2 mod n ---> ai2
% n
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page 415 line -1: eit ---> ei,t+1
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page 416 line 2: ct ---> ct+1
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page 416 line 3: ctvt ---> ct+1vt+1
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page 416 line 8: pi ---> pj
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page 416 line -16: F2t ---> F2t+1
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page 416 line -3: satisying ---> satisfying
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page 417 line -1: bi ---> b
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page 418 line 2: bi ---> b
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page 419 line 11: 14 ---> 12
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page 421 line 10: q(x) ---> q(x) = (x+m)2 - n
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page 421 line 13: [insert] (We will take ai = x+m .)
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page 424 line 14: upon upon ---> upon
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page 426 line -18: I ---> the ideal generated by x2+1
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page 433 line 3: (0,b0%p) ---> (0,b0%p), (1,b1%p)
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page 433 line -15: (0,b0) ---> (0,b0%29)
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page 433 line -5: (0,b0) ---> (0,b0%101)
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page 434 line 11: (2-9)7) ---> (2-9)7
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page 436 line -5: ['Z' should be boldfaced, twice]
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page 437 line -11: square ---> squares
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page 438 line 4: pair ---> pairs
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page 438 line -14: pair ---> pairs
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page 439 line 8: divisionx ---> divisions
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page 439 line 10: P) ---> P
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page 439 line -12: either of in ---> in either of
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page 439 [Example is incorrect: 1+x lies in the intersection...]
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page 440 [Example is incorrect: 1+x lies in the intersection...]
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page 440 line 15: either of in ---> in either of
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page 442 line -10: unsuccesful ---> unsuccessful
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page 448 line 12: possible ---> possibly
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page 449 line -14: intersect ---> intersects
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page 487 line 6: will try ---> will not try
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page 488 line 7: 1 ---> idB
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page 489 line 11: an an ---> an
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page 491 line 13: length L1 + length L1 ---> length
L1 + length L2
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page 491 line 18: length L1 + length L1 ---> length
L1 + length L2
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page 493 line -12: (x1,x2)to ---> (x1,x2)
to [add space]
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page 493 line -9: (x1,x2,x3)to ---> (x1,x2,x3)
to [add space]
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page 498 line -22: it's ---> its
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page 509 line 1: 2, 3, 5, 7 ---> 3, 5, 7
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page 511 line [in: header] Roots ---> Roots of Primes
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page 511 line 1: Roots ---> Roots of Primes
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page 516 3.3.05 [lower line of permutation] 5 1 7 2 7 6 3 ---> 5 1 4 2
7 6 3
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page 517 7.8.03 29%11=3 ---> 28%11=3, 29%11=6
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page 517 12.1.06 3 ---> 1
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page 517 12.4.02 500, 111 ---> 500111
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page 517 12.4.02 14, 197 ---> 14197
© 1996-2002, Paul Garrett