A number k such that n k^2 has its last digit(s) equal to k is called n-automorphic. For example, 1·(5__)^2 = 25__ and 1·(6__)^2 = 36__, so 5 and 6 are 1-automorphic. Similarly, 2·(8__)^2 = 128__ and 2·(88__)^2 = 15488__, so 8 and 88 are 2-automorphic. de Guerre and Fairbairn give a history of automorphic numbers.

idempotent | narcissistic number | number pyramid | trimorphic number