One of the mysteries of the English language finally explained.
1Mathematics. 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).
2Characterized by automorphism; formed on oneself.
4Mathematics. 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.
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.
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