A Converse of Fermat's Little Theorem

Autor/in	Bruckman, P. S.
Titel	A Converse of Fermat's Little Theorem
Quelle	In: International Journal of Mathematical Education in Science and Technology, 38 (2007) 4, S.554-555 (2 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0020-739X
Schlagwörter	Numbers; Algebra; Mathematical Formulas; Theories; Mathematical Logic; Validity + Suchen Sie Ihr Suchwort? Zahlenraum; Mathematische Formel; Theory; Theorie; Mathematical logics; Mathematische Logik; Gültigkeit
Abstract	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). (Author).
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Update	2017/4/10