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.

(In reply to solution by xdog)

For any pair of distinct odd primes p and q, the value p*q^(k-1) has exactly k distinct factorizations.

Posted by Brian Smith on 2018-12-31 11:56:39