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

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asked Oct 20, 2017 at 11:24

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

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.

nt.number-theory