On the difference of values of the kernel function at consecutive integers

Jean-Marie De Koninck and Florian Luca

International Journal of Mathematics and Mathematical Sciences, 2003, vol. 2003, 1-14

Abstract:

For each positive integer n , set γ ( n ) = Π p | n p . Given a fixed integer k ≠ ± 1 , we establish that if the A B C -conjecture holds, then the equation γ ( n + 1 ) − γ ( n ) = k has only finitely many solutions. In the particular cases k = ± 1 , we provide a large family of solutions for each of the corresponding equations.

Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:648401

DOI: 10.1155/S016117120330403X

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