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a @ b =(a-b)/ gcd(a,b)

Source: Estonia IMO TST 2010 p1

April 1, 2020
number theoryGCDprimespower of primecoprime

Problem Statement

For arbitrary positive integers a,ba, b, denote a@b=a−bgcd(a,b)a @ b =\frac{a-b}{gcd(a,b)} Let nn be a positive integer. Prove that the following conditions are equivalent: (i) gcd(n,n@m)=1gcd(n, n @ m) = 1 for every positive integer m<nm < n, (ii) n=pkn = p^k where pp is a prime number and kk is a non-negative integer.
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