Show your works please.

1.1) Theorem A. There are no integer solutions to the Diophantine equa tion 22 +5y2 14. By integer solutions we mean the domain of x and y are Z. Proof Theorem A by Contradiction 1.2) Theorem B. Prove that Var(2,2 + )2 2, where domain of x is R+. Proof theorem B and also state your proving methodology 1.3) Theorem C. Prove that between every rational number and every irrational number there is an irrational number Proof Theorem C by Contradiction 1.4) Theorem D. If a, b E Z and a