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5. Let a, b e Z and n 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.)

5. Let a, b e Z and n 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.)

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 6TFE: Label each of the following statements as either true or false. If ab0(modn), then either a0(modn)...
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Let a, b E Z and n E Z+. Prove that if a = b(mod n), then ged(a,n) = ged(b, n).

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.) 5.
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.) 5.
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