Prof wrote this:
$ \mathsf x^2 + 1 \equiv 0 mod 65 $
His next step is
$ \mathsf x^2 - 64 \equiv 0 (65) $
How did it got there? I mean, i presume that $ \mathsf x = 8 $ because 64+1 = 65 and 65 divided is 1 with no remainder. But how and why did he wrote it like that?
From
$ \mathsf x^2 - 64 \equiv 0 (65) $
He goes to $ \mathsf x^2 - 8^2 \equiv 0 (65) $
Factorizes to $ \mathsf (x-8)(x+8) \equiv 0 (65) $
And i get the factorization but not how he moved the 8 and 64, any tips?
EDIT: still didn't use Fermat Little Theorem or Euleros Theorem.