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Let a, b e Z and n E Z*. Prove that if a = b(mod n), then gcd(a, n) = gcd(b, n).

Let a, b e Z and n E Z*. Prove that if a = b(mod n), then gcd(a, n) = gcd(b, n).

Elements Of Modern Algebra
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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Let a, b e Z andn E Z*. Prove that if a = b(mod n), then gcd(a, n) = gcd(b, n). (Hint: use the fact that if an integer d divides two numbers, then d divides any integer combination of those two numbers.)
Transcribed Image Text:Let a, b e Z andn E Z*. Prove that if a = b(mod n), then gcd(a, n) = gcd(b, n). (Hint: use the fact that if an integer d divides two numbers, then d divides any integer combination of those two numbers.)
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