Given that a is a quadratic reisdue of the odd prime p, prove the following: b) The integer p - a is a quadratic residue or nonresidue of p according as p=1 (mod 4) or p=3 (mod 4). c) If p = 3 (mod 4) then x ± a^((P+1)/4)) (mod p) are the solutions of the congruence x^(2) = a (mod p).

Given that a is a quadratic reisdue of the odd prime p, prove the following: b) The integer p - a is a quadratic residue or nonresidue of p according as p=1 (mod 4) or p=3 (mod 4). c) If p = 3 (mod 4) then x ± a^((P+1)/4)) (mod p) are the solutions of the congruence x^(2) = a (mod p).

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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