automorphic
/ˌɔːtə(ʊ)ˈmɔːfɪk/adjective
1 Mathematics. Of a function: invariant with respect to a group of linear transformations of a certain kind. Of a transformation: †leaving a certain function invariant ( obsolete ).
- In modern use, if a function f(x) is automorphic with respect to a group G, then f(T n(x)) = f(x) for every element T n of G. This use originated with F. Klein..
2Characterized by automorphism; formed on oneself.
3 Crystallography = idiomorphic rare.
4 Mathematics. Designating an n-digit number which when raised to a power gives a number whose last n digits are the same as the original number.
- E.g. 5 is automorphic because 52 is 25, 53 is 125, 54 is 625, etc.; 76 is automorphic because 762 is 5776, 763 is 438,976, etc..
Origin
Mid 19th century; earliest use found in Arthur Cayley (1821–1895), mathematician. From auto- + -morphic. In the mathematical use designating a function after German automorph.