2
$\begingroup$

I recently came accross the Wolstenholme theorem which says that $$\binom{ap}{bp} \equiv \binom{a}{b} \pmod {p^{3}}$$ On wikipedia, it gives a combinatorial proof of this theorem that involves splitting a set A of size ap into a rings of size p, but I don't understand the rest of the proof. Can someone help breakdown the group theory in that proof? I'm familiar with what a direct sum and what the cyclic group is, but I don't understand this proof.

$\endgroup$

Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Browse other questions tagged or ask your own question.