(a) Suppose that rị and r2 are quadratic non-residues modulo an odd prime p. Does x = r¡r2 (mod p) have a solution? (b) Suppose r is a quadratic non-residues modulo odd primes p and q. Does x? = r (mod pq) have a solution?

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.5: Congruence Of Integers
Problem 58E: a. Prove that 10n(1)n(mod11) for every positive integer n. b. Prove that a positive integer z is...
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(a) Suppose that ri and r2 are quadratic non-residues modulo an odd prime p. Does a? = r1r2 (mod p) have a
solution?
(b) Suppose r is a quadratic non-residues modulo odd primes p and q. Does x? = r (mod pg) have a solution?
Transcribed Image Text:(a) Suppose that ri and r2 are quadratic non-residues modulo an odd prime p. Does a? = r1r2 (mod p) have a solution? (b) Suppose r is a quadratic non-residues modulo odd primes p and q. Does x? = r (mod pg) have a solution?
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