Every odd composite $=$ prime ${}+ 2x^2$ 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.
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.
Starting from $p_{n}=3$

Every odd composite $N$ can be written as $N= p^2_{n}+ 2p_{n}c$

Ex for $p_{n}=5$

$25 + 10c =N$

For $c$ from 0 to 7 we have the set of odd composites $[25,35,45,55,65,75,85]$

Intuitively $N= p^2_{n}+ 2p_{n}c$ can't be equal to $N= p_{n}+ 2x^2$