Suppose that $ k,l $ are natural numbers such that $ \gcd (11m-1,k)=\gcd (11m-1, l) , $ for any natural number $ m. $ Prove that there exists an integer $ n $ such that $ k=11^nl. $
Problem
Source: Romanian TST 1978, Day 1, P2
Tags: number theory, greatest common divisor, GCD, modular arithmetic