Path To College Mathematics, Books A La Carte Edition Plus Mylab Math Student Access Kit
1st Edition
ISBN: 9780134618555
Author: Elayn Martin-Gay
Publisher: PEARSON
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Chapter C, Problem 48ES
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To write
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Without evaluating the Legendre symbols, prove the following.
(i) 1(173)+2(2|73)+3(3|73) +...+72(72|73) = 0.
(Hint: As r runs through the numbers 1,2,.
(ii) 1²(1|71)+2²(2|71) +3²(3|71) +...+70² (70|71)
= 71{1(1|71) + 2(2|71) ++70(70|71)}.
72, so does 73 – r.)
By considering the number N = 16p²/p... p² - 2, where P1, P2, … … … ‚ Pn
are primes, prove that there are infinitely many primes of the form
8k - 1.
(c) (i) By first considering the case where n is a prime power, prove that
n
μ² (d)
=
ø(n)
(d)'
n≥ 1.
d\n
(ii) Verify the result of part (c)(i) when n =
20.
Chapter C Solutions
Path To College Mathematics, Books A La Carte Edition Plus Mylab Math Student Access Kit
Ch. C - Prob. 1ESCh. C - Prob. 2ESCh. C - Prob. 3ESCh. C - Prob. 4ESCh. C - Prob. 5ESCh. C - Prob. 6ESCh. C - Prob. 7ESCh. C - Prob. 8ESCh. C - Prob. 9ESCh. C - Prob. 10ES
Ch. C - Prob. 11ESCh. C - Prob. 12ESCh. C - Prob. 13ESCh. C - Prob. 14ESCh. C - Prob. 15ESCh. C - Prob. 16ESCh. C - Prob. 17ESCh. C - Prob. 18ESCh. C - Prob. 19ESCh. C - Prob. 20ESCh. C - Prob. 21ESCh. C - Prob. 22ESCh. C - Prob. 23ESCh. C - Prob. 24ESCh. C - Prob. 25ESCh. C - Prob. 26ESCh. C - Prob. 27ESCh. C - Prob. 28ESCh. C - Prob. 29ESCh. C - Prob. 30ESCh. C - Prob. 31ESCh. C - Prob. 32ESCh. C - Prob. 33ESCh. C - Prob. 34ESCh. C - Prob. 35ESCh. C - Prob. 36ESCh. C - Prob. 37ESCh. C - Prob. 38ESCh. C - Prob. 39ESCh. C - Prob. 40ESCh. C - Prob. 41ESCh. C - Prob. 42ESCh. C - Prob. 43ESCh. C - Prob. 44ESCh. C - Prob. 45ESCh. C - Prob. 46ESCh. C - Prob. 47ESCh. C - Prob. 48ESCh. C - Prob. 49ESCh. C - Prob. 50ESCh. C - 12,000 good assembly line products to 40 defective...Ch. C - Prob. 52ESCh. C - Prob. 53ESCh. C - Prob. 54ESCh. C - Prob. 55ESCh. C - Prob. 56ESCh. C - Prob. 57ESCh. C - Prob. 58ESCh. C - Prob. 59ESCh. C - Prob. 60ESCh. C - Prob. 61ESCh. C - Prob. 62ESCh. C - Prob. 63ESCh. C - Prob. 64ESCh. C - Prob. 65ESCh. C - Prob. 66ESCh. C - Prob. 67ESCh. C - Prob. 68ESCh. C - Prob. 69ESCh. C - Prob. 70ES
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