Publications de l’Institut Mathématique, Nouvelle Série, Vol. 100[114], No. 1/1, pp. 101

Publications de l’Institut Mathématique, Nouvelle Série
Vol. 100[114], No. 1/1, pp. 101–106 (2016)

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ON DISTINCT RESIDUES OF FACTORIALS

Vladica Andrejić, Miloš Tatarević

Faculty of Mathematics, University of Belgrade, Belgrade, Serbia; Alameda, CA 94501, USA

Abstract: We investigate the existence of primes $p > 5$ for which the residues of $2!$ , $3!$ , ..., $(p - 1)!$ modulo $p$ are all distinct. We describe the connection between this problem and Kurepa’s left factorial function, and report that there are no such primes less than $10^{11}$ .

Keywords: left factorial; factorial; prime numbers

Classification (MSC2000): 11B83; 11K31

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Electronic fulltext finalized on: 8 Nov 2016. This page was last modified: 14 Nov 2016.

© 2016 Mathematical Institute of the Serbian Academy of Science and Arts
© 2016 FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition