We solve the enumeration of the set AP(n) of partitions of a positive integer n in which the nondecreasing sequence of parts forms an arithmetic progression. In particular, we establish a formula for the number of nondecreasing arithmetic progressions of positive integers with sum n. We also present an explicit method to calculate all the partitions of AP(n).

partition, arithmetic progression, arithmetic generated by a sequence.

Received: November 16, 2021; Accepted: December 31, 2021; Published: January 21, 2022

How to cite this article: F. Javier de Vega, A complete solution of the partition of a number into arithmetic progressions, JP Journal of Algebra, Number Theory and Applications 53(2) (2022), 109-122. DOI: 10.17654/0972555522006

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License 

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