I was trying to work out whether or not 2n+3 divides (2n+1)! for positive integers n. After trying a few cases I think it does not work but I don't know how a proof for this would work. I tried induction but it got really messy. I also tried rephrasing it, such as putting it into modular equation but have had no luck.(adsbygoogle = window.adsbygoogle || []).push({});

My other question is about a congruence. The statement is that (1-x)^{p-1}is congruent to 1 + x + ... + x^{p-2}+ x^{p-1}modulo p where p is an odd prime. I tried to use the binomial theorem to prove this but couldn't finish it because it got really messy and also I have no experience in number theory. Any in understanding and working out these statements would be appreciated.

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# Divisibility and Congruence problem

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