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)

...." n=k^k isn't big enough and n=k^2k fails for even k, but n=k^3k allows at least k matches.  

Posted by Ady TZIDON on 2018-12-31 11:22:25