1.) Compute the squares modulo 23 as efficiently as possible.
2.) Show that $y^2 = 23x^2 + 7$ has no integer solutions.
This is a two part problem on my review for number theory and I am a bit lost. After going to my professor with this his hint was for part 2 saying to reduce it to mod 23. Having a really tough time with this problem any help is greatly appreciated.