I am working on a school assignment and I am being asked to solve the following:
Let A be the set of all integers x such that x is = k2 for some integer k
Let B be the set of all integers x such that the square root of x, SQRT(x), is an integer
Give a formal proof that A = B. Remember you must prove two things: (1) if x is in A, then x is in B, AND (2) if x is in B, then x is in A
I have done proofs before in my class that involved first proving that certain terms were odd or even and then algebraically reducing to a final proof, but I am not sure of how to go about proving this one. Any help will be appreciated. Thank you.