I'm having a hard time solving two problems I've been looking at for a while, they both involve Eulers theorem and Fermat's Little Theorem, here they are: Let p ≡ 3 (mod 4 ) be prime. Show that x^2 ≡ -1 (mod p) has no solutions. (Hint: Suppose x exists. Raise both sides to the power (p - 1)/2 and use Fermat's theorem). The other problem is this: Let n = 84047 * 65497. Find x and y with x^2 ≡ y^2 (mod n) but x ≠(the symbol should be not congruent, couldn't find the symbol) +- (plus or minus) y mod n. I've been looking at these for 2 hours and I don't know how to solve these. Any ideas? If you show the solution, please explain how if possible, thanks!