I was looking through some project-euler questions and I came across one that said
Every odd composite number can be written as the sum of a prime and twice a square…This was proven false.
So, I solved the problem through brute-force in Java but I was wondering how I can do this on paper? Please don't give me the answer, just some hints
Thanks.
Best Answer
Some proofs that a number-theoretic statement like that isn't true basically amount to finding a counterexample. That isn't to say there isn't an elegant analytic approach, but the claim that this was proven false might simply be a reference to the fact that someone has found a number which can't be written in that way, and shown that it fits by brute force as well.