Two congruences involving 4-cores

Michael D. Hirschhorn; James Allen Sellers

Two congruences involving 4-cores

Michael D. Hirschhorn, James Allen Sellers

Mathematics

Research output: Contribution to journal › Article › peer-review

23 Scopus citations

Abstract

The goal of this paper is to prove two new congruences involving 4-cores using elementary techniques; namely, if a₄(n) denotes the number of 4-cores of n, then a₄(9n + 2) ≡ 0 (mod 2) and a₄(9n + 8) ≡ 0 (mod 4).

Original language	English (US)
Article number	R10
Pages (from-to)	1-8
Number of pages	8
Journal	Electronic Journal of Combinatorics
Volume	3
Issue number	2 R
State	Published - 1996

All Science Journal Classification (ASJC) codes

Discrete Mathematics and Combinatorics

Cite this

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title = "Two congruences involving 4-cores",

abstract = "The goal of this paper is to prove two new congruences involving 4-cores using elementary techniques; namely, if a4(n) denotes the number of 4-cores of n, then a4(9n + 2) ≡ 0 (mod 2) and a4(9n + 8) ≡ 0 (mod 4).",

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year = "1996",

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AU - Sellers, James Allen

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AB - The goal of this paper is to prove two new congruences involving 4-cores using elementary techniques; namely, if a4(n) denotes the number of 4-cores of n, then a4(9n + 2) ≡ 0 (mod 2) and a4(9n + 8) ≡ 0 (mod 4).

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AN - SCOPUS:0040996886

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Two congruences involving 4-cores

Abstract

All Science Journal Classification (ASJC) codes

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