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M.Tamba, On a partition function which assumes all integral values, J.Number Theory 41 (1992) 77-86.

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Article

Note on a Partition Function Which Assumes All Integral Values

1Department of Mathematics, Goa University, Taleigao Plateau, Goa, India


Turkish Journal of Analysis and Number Theory. 2014, Vol. 2 No. 6, 220-222
DOI: 10.12691/tjant-2-6-5
Copyright © 2014 Science and Education Publishing

Cite this paper:
Manvendra Tamba. Note on a Partition Function Which Assumes All Integral Values. Turkish Journal of Analysis and Number Theory. 2014; 2(6):220-222. doi: 10.12691/tjant-2-6-5.

Correspondence to: Manvendra  Tamba, Department of Mathematics, Goa University, Taleigao Plateau, Goa, India. Email: tamba@unigoa.ac.in

Abstract

Let G(n) denote the number of partitions of n into distinct parts which are of the form 2m, 3m, 5m, 6m-3, 8m-3, 9m-3 or 11m-3 with parts of the form 2m, 3m, 6m-3, or 11m-3 being even in number minus the number of them with parts of the form 2m, 3m, 6m-3, or 11m-3 being odd in number. In this paper, we prove that G(n) assumes all integral values and does so infinitely often.

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