I have three proofs that I am not really sure how to do. I will provide you with what I have so far, if you could please fill in the holes that would be great.

1) Prove that the product of two consecutive integers is even.

Pf: Let x,y be integers such that y = x + 1. Then xy = x(x+1) = x^2+x. There exists some integer c such that c = 2|(x^2+x).

2) For x > 0 and y>o, prove that x < y if and only if x^2 < y^2

=> If x < y then x^2 < y^2.

Pf: Let x and y be integers such that y = x +5. x^2 = x^2 and y^2 = (x+5)^2 = x^2 + 10x + 25.

<= if x^2 < y^2 then x < y

Pf: Let x^2 and y^2 be integers such that y^2 = x^2 + 1.

3) For n>2 prove or dispirove that n^2 -1 is composite.