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TOT 2000 Spring AS1 max of gcd of m + 2000n and n + 2000m

Source:

May 11, 2020

number theorygreatest common divisor

Problem Statement

Positive integers

m

and

n

have no common divisor greater than one. What is the largest possible value of the greatest common divisor of

m + 2000n

and

n + 2000m

?
(S Zlobin)