Consider the following universal statement. The sum of any two perfect squares between 1 and 20 is composite. Give a counterexample which proves that the statement is false.

It is easy to show that 3 is not the sum of the + b² ± 3 squares of 2 integers, i.e. a² for any integers a and b. Prove that there are infinitely many such integers that cannot be written as the sum of the squares of two integers. a² + b² # 6 a² + b² ± 7 a² + b² # 11

Prove the following statements using any type of the following: Direct ProofContrapositive ProofProof by ContradictionProving Non-Conditional Statements Note: please determine which proof you will be using.