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Bounds for frequencies of residues of second-order recurrences modulo p r

Walter Carlip, Lawrence Somer (2007)

Mathematica Bohemica

The authors examine the frequency distribution of second-order recurrence sequences that are not p -regular, for an odd prime p , and apply their results to compute bounds for the frequencies of p -singular elements of p -regular second-order recurrences modulo powers of the prime p . The authors’ results have application to the p -stability of second-order recurrence sequences.

Bounds for the counting function of the Jordan-Pólya numbers

Jean-Marie De Koninck, Nicolas Doyon, A. Arthur Bonkli Razafindrasoanaivolala, William Verreault (2020)

Archivum Mathematicum

A positive integer n is said to be a Jordan-Pólya number if it can be written as a product of factorials. We obtain non-trivial lower and upper bounds for the number of Jordan-Pólya numbers not exceeding a given number x .

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