AN INTRODUCTION TO THE THEORY OF NUMBERS Fifth Edition, Corrected Printings by Ivan Niven Herbert S. Zuckerman Hugh L. Montgomery

John Wiley (New York), 1991

ERRATA AND REVISIONS FOR PRINTINGS 3 AND HIGHER

PAGE/LINE

v/−15..−6 In place of the passage ‘The instructor may … subdirectory /pub/clint.’

subsitute:

Instructors can obtain a set of solutions to the starred exercises by contacting the third author, whose web page also provides useful software, a manual of computational laboratories, and several supplements.

vi/11  for ‘Appendixes’ read ‘Appendices’
1/12,13  replace ‘natural number such as’ by

‘natural number greater than 1 such as’

1/−2  replace ‘any exponent’ by ‘any integral exponent’
2/5  replace ‘natural numbers’ by ‘integers’
3/−10,−11 replace ‘is a logical consequence of the first’ by

‘is logically equivalent to the first’

18/3  between ‘of’ and ‘integers’ insert ‘two or more’.
29/−3  replace ‘numbers n’ by ‘numbers n ≥ 4’

[Thanks to Art Benjamin for pointing this out.]

56/2  Replace ‘ad − bc’ by ‘ad + bc’
57/Exercise 14replace ‘all n’ by ‘all n ≥ 0’
88/6  replace ‘f′(5) = 1 ≢ 0 (mod 7)’ by ‘f′(5) = 11 ≢ 0 (mod 7)’

[Thanks to Peter Kahn for pointing this out.]

102/1  The term ‘quadratic residue’ is defined in Definition 3.1 on page 131.
107/4  replace ‘p|(a^{2n} + 1)’ by ‘p|(a^{2^{n}} + 1)’
110/−2  The term ‘quadratic nonresidue’ is defined in Definition 3.1 on page 131.
137/^{∗}22.  Replace ‘(p + 1)^{1/2}’ by ‘p − 1’
157/−4  Replace ‘ax^{2} + bxy + y^{2}’ by ‘ax^{2} + bxy + cy^{2}’

NZM corrections, continued

161/15  To the end of the definition append: ‘(When d < 0, we count

/it only the positive definite forms.)’

182/1  Replace ‘de Plignac’s formula.’ by ‘(Legendre)’
195/Problem 5Replace ‘2^{ω(n).}’ by ‘2^{ω(n)}.’
197/-8  for ‘Slow’ read ‘Show’
207/13  Replace ‘permits’ by ‘permutes’
237/10  Replace ‘(−1, 1), (0, 1), (3, 11),’ by ‘(−1, ±1), (0, ±1), (3, ±11)’
293/−20  replace ‘Section 1.1’ by ‘Section 1.2’

[Thanks to Harley Flanders for pointing this out.]

308/6  Replace ‘\sqrt{5}’ by ‘^{3} \sqrt{5}’
318  Between Corollary 6.27 and its proof, insert the following paragraph:

With a small amount of calculation one can show that 33 is not the sum of five positive perfect squares, but that every integer n, 34 ≤ n ≤ 169, is the sum of five positive squares. Hence the constant 169 in the corollary above can be replaced by 33, but not by any smaller number. [Thanks to P. T. Bateman for suggesting this.]

321/12  Wrong font: ‘bf_{1} = g’ should be ‘bf_{1} = g’
356/−7  Replace ‘x_{2} = y_{2}\sqrt{d}’ by ‘x_{2} + y_{2}\sqrt{d}’

[Thanks to Greg Martin for pointing this out.]

448/−1  Replace ‘q^{e}(n) = q^{o}(n)’ by ‘q^{e}(n) − q^{o}(n)’

[Thanks to Greg Martin for pointing this out.]