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

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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.

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Authors and Affiliations

  1. Institute of Information and Mathematical Sciences, Massey University, Private Bag 102904, North Shore Mail Centre, Auckland, New Zealand

    Shaun Cooper

  2. School of Mathematics, University of New South Wales, Sydney, 2052, Australia

    Michael Hirschhorn

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  1. Shaun Cooper
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  2. Michael Hirschhorn
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Correspondence to Shaun Cooper.

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Dedicated to Richard Askey on the occasion of his 70th birthday.

2000 Mathematics Subject Classification Primary—11E25; Secondary—05A15, 33E05.

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Cooper, S., Hirschhorn, M. On the number of primitive representations of integers as sums of squares. Ramanujan J 13, 7–25 (2007). https://doi.org/10.1007/s11139-006-0240-6

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