**ERIC Number:**EJ771151

**Record Type:**Journal

**Publication Date:**2007-Jun

**Pages:**2

**Abstractor:**Author

**ISBN:**N/A

**ISSN:**ISSN-0020-739X

A Converse of Fermat's Little Theorem

Bruckman, P. S.

International Journal of Mathematical Education in Science and Technology, v38 n4 p554-555 Jun 2007

As the name of the paper implies, a converse of Fermat's Little Theorem (FLT) is stated and proved. FLT states the following: if p is any prime, and x any integer, then x[superscript p] [equivalent to] x (mod p). There is already a well-known converse of FLT, known as Lehmer's Theorem, which is as follows: if x is an integer coprime with m, such that x[superscript m-1] [equivalent to] 1 (mod m), and if there exists no integer e less than m-1 such that x[superscript e] [equivalent to] 1 (mod m), then m is prime. The new converse in question states the following: if p is any prime and x[superscript p] [equivalent to] x (mod p), where x is known only to be algebraic, then x must be an integer (mod p).

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**Publication Type:**Journal Articles; Reports - Descriptive

**Education Level:**N/A

**Audience:**N/A

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A