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|State whether the following statements are true or false. Show working. a. For each odd prime p, a residue a in Z*p cannot be both a primitive root and a quadratic residue. b. The integer 2 has a quadratic residue modulo the prime 399989. c. If p, q are odd primes and pg = 1 mod 4, then -1 has a quadratic residue modulo at least one of p or q.

|State whether the following statements are true or false. Show working. a. For each odd prime p, a residue a in Z*p cannot be both a primitive root and a quadratic residue. b. The integer 2 has a quadratic residue modulo the prime 399989. c. If p, q are odd primes and pg = 1 mod 4, then -1 has a quadratic residue modulo at least one of p or q.

Advanced Engineering Mathematics
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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|State whether the following statements are true or false. Show working. a. For each odd prime p, a residue a in Z*p cannot be both a primitive root and a quadratic residue. b. The integer 2 has a quadratic residue modulo the prime 399989. c. If p, q are odd primes and pg = 1 mod 4, then -1 has a quadratic residue modulo at least one of p or q.
Transcribed Image Text:|State whether the following statements are true or false. Show working. a. For each odd prime p, a residue a in Z*p cannot be both a primitive root and a quadratic residue. b. The integer 2 has a quadratic residue modulo the prime 399989. c. If p, q are odd primes and pg = 1 mod 4, then -1 has a quadratic residue modulo at least one of p or q.
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