Let p and q be distinct odd primes such that gcd(p−1, q−1) = 2. Does there exist an integer M such that aM ≡ a-1 (mod p) and aM ≡ a (mod q) for all a ∈ (Z/pqZ)*? What if gcd(p−1, q−1) > 2?
Let p and q be distinct odd primes such that gcd(p−1, q−1) = 2. Does there exist an integer M such that aM ≡ a-1 (mod p) and aM ≡ a (mod q) for all a ∈ (Z/pqZ)*? What if gcd(p−1, q−1) > 2?
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.4: Prime Factors And Greatest Common Divisor
Problem 5E: Prove that if p and q are distinct primes, then there exist integers m and n such that pm+qn=1.
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Let p and q be distinct odd primes such that gcd(p−1, q−1) = 2. Does there exist an integer M such that aM ≡ a-1 (mod p) and aM ≡ a (mod q) for all a ∈ (Z/pqZ)*? What if gcd(p−1, q−1) > 2?
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