Quadratic reciprocity
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I need help with this problem:
(a) If p is an odd prime and q is an odd prime where q = 10p + 3, show that (p/q)=(3/p).
(b) If p is an odd prime and q is an odd prime where q = 10p + 1, show that (p/q)=(-1/p).
Please show all work so that I understand each step. Thanks for the help.
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Solution Summary
Quadratic reciprocity is analyzed.
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Proof:
(a) If both p and q are odd primes with q = 10p + 3, then we have two cases.
Case 1: p = 1 (mod 4), then (p/q) = (q/p) = ((10p + 3)/p) = (3/p)
Case 2: p = 3 (mod 4), then p = 4k + 3, then q = 10p + 3 = ...
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