SOME RESULTS ON ORDERED AND UNORDERED FACTORIZATION OF A POSITIVE INTEGER

Document Type : Original Manuscript

Authors

1 Department of Computer science, University of Torbat e Jam, Torbat e Jam, Iran.

2 Department of Pure Mathematics, University of Ferdowsi, Mashhad, Iran.

Abstract

A well-known enumerative problem is to count the number of ways a positive integer $n$ can be factorised as $n=n_1\times n_2\times\cdots\times n_{k}$, where $n_1\geqslant n_2 \geqslant \cdots \geqslant n_{k} >1$. In this paper, we give some recursive formulas for the number of ordered/unordered factorizations of a positive
integer $n$ such that each factor is at least $\ell$. In particular, by using elementary techniques, we give an explicit formula in cases where $k=2,3,4$.

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References

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Journal of Algebraic Systems
Volume 12, Issue 2
January 2025
Pages 257-267

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