Let k be a positive integer.
Prove that there must exist a positive integer n such that the sets A( A={1^2, 2^2, 3^2, . . . }) and B ( B = {1^2+n, 2^2+n, 3^2+n, . . . }) share k identical members.

The task is to pick n so that a^2 = b^2 + n has k solutions for a given k when a and b range over the positive integers.

Posted by xdog on 2018-12-31 08:48:09