The Center for Education and Research in Information Assurance and Security (CERIAS)

The Center for Education and Research in
Information Assurance and Security (CERIAS)
Center for Education and Research in Information Assurance and Security

Congruences for $r_s(n)$ modulo $2s$

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Author

Samuel S Wagstaff Jr

Tech report number

CERIAS TR 2007-84

Entry type

article

Abstract

Let $r_s(n)$ denote the number of ways to write $n$ as the sum of $s$ squares of integers. The paper determines $r_s(n)$ modulo $2s$ when $s$ is prime or a power of 2. For general $s$ it gives a congruence for $r_s(n)$ modulo the highest power of 2 dividing $2s$.

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Date

2007

URL

http://dx.doi.org/10.1016/j.jnt.2007.05.002

Journal

Journal of Number Theory

Key alpha

Wagstaff

Pages

326-329

Volume

127

Affiliation

Purdue University

Publication Date

2001-01-01

Subject

congruences for the number of ways to write an integer as the sum of a fixed number of squares of integers

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