Searching for a counterexample to Kurepa’s conjecture
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- by Vladica Andrejić and Milos Tatarevic PDF
- Math. Comp. 85 (2016), 3061-3068 Request permission
Abstract:
Kurepa’s conjecture states that there is no odd prime $p$ that divides $!p=0!+1!+\cdots +(p-1)!$. We search for a counterexample to this conjecture for all $p<2^{34}$. We introduce new optimization techniques and perform the computation using graphics processing units. Additionally, we consider the generalized Kurepa’s left factorial given by $!^{k}n=(0!)^k +(1!)^k +\cdots +((n-1)!)^{k}$, and show that for all integers $1<k<100$ there exists an odd prime $p$ such that $p\mid !^k p$.References
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Additional Information
- Vladica Andrejić
- Affiliation: Faculty of Mathematics, University of Belgrade, Belgrade, Serbia
- MR Author ID: 789950
- Email: andrew@matf.bg.ac.rs
- Milos Tatarevic
- Affiliation: Alameda, California 94501
- Email: milos.tatarevic@gmail.com
- Received by editor(s): September 2, 2014
- Received by editor(s) in revised form: March 31, 2015, and June 17, 2015
- Published electronically: March 24, 2016
- Additional Notes: This work was partially supported by the Serbian Ministry of Education and Science, project No. 174012
- © Copyright 2016 American Mathematical Society
- Journal: Math. Comp. 85 (2016), 3061-3068
- MSC (2010): Primary 11B83; Secondary 11K31
- DOI: https://doi.org/10.1090/mcom/3098
- MathSciNet review: 3522982