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In mathematics, an automorphic number (sometimes referred to as a circular number) is a number whose square "ends" in the same digits as the number itself. For example, 42 = 14, 692 = 3969, 38542 = 11873854, X083692 = 851X4EX08369, so 4, 69, 3854, and X08369 are all automorphic numbers.

The first few are automorphic numbers are

0, 1, 4, 9, 54, 69, 369, 854, 3854, 8369, E3854, 1E3854, X08369, 5X08369, 61E3854, E61E3854, 1E61E3854, X05X08369, 21E61E3854, ...

These numbers are the "infinite" solution of x2 − x = 0. In fact, they are the solution of this equation in the ring of dozadic (10-adic) numbers.