Show that if p is an odd prime, then is a multiple of p.
I tried to do this using recursion, but I failed to do so because I couldn't complete the
"if hypotheses is true for nth prime then it holds for the (n+1)th prime" step,
since I can't explicitly write down what the next prime is.
I tried to do a combinatorial approach of "distributing p distinct objects into p-1 identical classes", but I couldn't see the connection.
So I would like some hints.
How should I use p's prime-ness in my proof?
Also, is a combinatorial proof possible?