Automorphic Number Checker

About this calculator

An automorphic number is a number whose square ends in the number itself. For example 5² = 25 (ends in 5), 6² = 36 (ends in 6), 25² = 625 (ends in 25), and 76² = 5776 (ends in 76). This calculator squares your number and checks whether the trailing digits of the result match the original number exactly.

Automorphic numbers are a classic topic in recreational number theory: they're closely tied to modular arithmetic (a number is automorphic in base 10 if n² ≡ n mod 10^d, where d is its digit count) and to idempotent elements in the ring of integers modulo 10^d. Number theory hobbyists, puzzle-solvers and programming-challenge enthusiasts use automorphic number checks to explore patterns in digit sequences and as a classic algorithm exercise — computing large squares and comparing trailing digits efficiently.