Automorphic number
In mathematics, an automorphic number (sometimes referred to as a circular number) is a natural number in a given number base b {\displaystyle b} whose square "ends" in the same digits as the number itself. == Definition and properties == Given a number base b {\displaystyle b} , a natural number n {\displaystyle n} with k {\displaystyle k} digits is an automorphic number if n {\displaystyle n} is a fixed point of the polynomial function f ( x ) = x 2 {\displaystyle f(x)=x^{2}} over Z / b k Z {\displaystyle \mathbb {Z} /b^{k}\mathbb {Z} } , the ring of integers modulo b k {\displaystyle b^{k}} .