The Ramanujan Journal

, Volume 13, Issue 1–3, pp 7–25 | Cite as

On the number of primitive representations of integers as sums of squares

Article

Abstract

Formulas for the number of primitive representations of any integer n as a sum of k squares are given, for 2 ≤ k ≤ 8, and for certain values of n, for 9 ≤ k ≤ 12. The formulas have a similar structure and are striking for their simplicity.

Keywords

Sum of squares Möbius inversion Generating function Divisor sum 

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© Springer Science + Business Media, LLC 2006

Authors and Affiliations

  1. 1.Institute of Information and Mathematical SciencesMassey UniversityAucklandNew Zealand
  2. 2.School of MathematicsUniversity of New South WalesSydneyAustralia

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