I need to show that there do not exist integers $a$ and $b$, both odd, for which $a^2+2$|$b^2+4$.
I have broken it into cases of $a>b$, $a=b$, and $a. The first two cases seem obvious, but I'm having difficulty figuring out where to go on the third case, assuming this is a reasonable approach. I have the feeling the legendre symbol might be of good use?