5. (a) Prove that if p > 3 is an odd prime, then if p = 1 (mod 6) (-3/p) = {-1 if p = 5 (mod 6) Scanned with CamScanner

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5 A Prove That If P 3 Is An Odd Prime Then If P 1 Mod 6 3 P 1 If P 5 Mod 6 Scanned With Camscanner 1 (30.92 KiB) Viewed 30 times

5. (a) Prove that if p > 3 is an odd prime, then if p = 1 (mod 6) (-3/p) = {-1 if p = 5 (mod 6) Scanned with CamScanner (b) Using part (a), show that there are infinitely many primes of the form 6k + 1. [Hint: Assume that P₁, P2...., p, are all the primes of the form 6k+ 1 and consider the integer N = (2P1 P₂ Pr)² +3.]