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show that there exist $n$ such that $$r|\binom{p^n}{q^n}$$

Cross-Posted from Math Stackexchange

Two positive integers $p,q$ and a prime $r$ are given, such that $r>p>q>1$.
I have to show that there exist $n$ such that $$r|\binom{p^n}{q^n}$$

Should I use Lucas' theorem? I can't solve it.

math110
  • 4.3k
  • 18
  • 46