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1. Let p be a prime and let g be a primitive root modulo p. Let a be an integer which is relatively Prove that a has a square root modulo p (i.e., there exists an integer b such that b² = a (mod p)) if and only if the discrete logarithm log, (a) is even. prime to p.

1. Let p be a prime and let g be a primitive root modulo p. Let a be an integer which is relatively Prove that a has a square root modulo p (i.e., there exists an integer b such that b² = a (mod p)) if and only if the discrete logarithm log, (a) is even. prime to p.

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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1. Let P be a prime and let g be a primitive root modulo p. Let a be an integer which is relatively prime to p. Prove that a has a square root modulo p (i.e., there exists an integer b such that b² = a (mod p)) if and only if the discrete logarithm log, (a) is even.
Transcribed Image Text:1. Let P be a prime and let g be a primitive root modulo p. Let a be an integer which is relatively prime to p. Prove that a has a square root modulo p (i.e., there exists an integer b such that b² = a (mod p)) if and only if the discrete logarithm log, (a) is even.
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