1. (20 points) Prove that every odd positive integer can be written as the difference of two squares (this means that, for every n0, there exist x and y, integers, such that 2n+ 1 = x2y2) 2. (20 points) Prove that every positive integer which is a multiple of 4 can be written as the difference of two perfect squares (this means that, for every n1, there exist x and y, integers, such that 4n= x2y2). 3. (20 points) Prove that, if n is an even number which is not a multiple of 4, then n cannot be written as the difference of two perfect squares.