IMO 1992 LL KOR43

Find the number of positive integers n satisfying arphi(n) | n such

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IMO 1992 LL KOR43

Origin: KOR

Problem

Find the number of positive integers n satisfying \varphi(n) | n such that \infty  m=1  n m −n −1 m  = 1992. What is the largest number among them? As usual, \varphi(n) is the number of positive integers less than or equal to n and relatively prime to n.6