Worlds of David Darling
Encyclopedia of Science
Home > Encyclopedia of Science

automorphic number

Also known as an automorph, a number n whose square ends in n. For instance 5 is automorphic, because 52 = 25, which ends in 5. A number n is called trimorphic if n3 ends in n. For example 493, = 117649, is trimorphic. Not all trimorphic numbers are automorphic. A number n is called tri-automorphic if 3n2 ends in n; for example 667 is tri-automorphic because 3 × 6672, = 1334667, ends in 667.

Related category