ADVANCED ENGINEERING MATH.>CUSTOM<
ADVANCED ENGINEERING MATH.>CUSTOM<
10th Edition
ISBN: 9781119480150
Author: Kreyszig
Publisher: WILEY C
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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.
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