Let a, b, c, m be integers with m > 2. Prove that if ac ≡ bc mod m and d = gcd(m, c) , then a ≡ b mod m/d.
Let a, b, c, m be integers with m > 2. Prove that if ac ≡ bc mod m and d = gcd(m, c) , then a ≡ b mod m/d.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.3: Divisibility
Problem 25E: Let ,, and be integers. Prove or disprove that implies or .
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Let a, b, c, m be integers with m > 2. Prove that if
ac ≡ bc mod m
and d = gcd(m, c) , then
a ≡ b mod m/d.
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