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.
show that there exist $n$ such that $r|\binom{p^n}{q^n}$
math110
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