Hi there, recently I came across the following divisibility question, and I wondered if much can be said about it. Let $p$ and $q$ be different primes, and suppose $p^n + q^r$ divides $p^{2m}  1$, where $n$, $m$, $r$ are positive integers, $n$ divides $m$, and $q^r > p^m$. Is a classification of the triples $(n,m,r)$ within reach ? Thanks !
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