Automorphic numbers

An automorphic number is a number whose square ends in the digits of the number itself. For example, 625 × 625 = 390625 ends in the digits 625, and 376 × 376 = 141376 ends in the digits 376. There are two trivial examples of automorphic numbers: 0 and 1. Apart from this, there is one hierarchy of examples ending in 5, and another hierarchy of examples e…