Greedy sums of distinct squares
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- by Hugh L. Montgomery and Ulrike M. A. Vorhauer PDF
- Math. Comp. 73 (2004), 493-513 Request permission
Abstract:
When a positive integer is expressed as a sum of squares, with each successive summand as large as possible, the summands decrease rapidly in size until the very end, where one may find two $4$’s, or several $1$’s. We find that the set of integers for which the summands are distinct does not have a natural density but that the counting function oscillates in a predictable way.References
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Additional Information
- Hugh L. Montgomery
- Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109-1109
- MR Author ID: 126550
- Email: hlm@umich.edu
- Ulrike M. A. Vorhauer
- Affiliation: Department of Mathematics, Kent State University, Kent, Ohio 44242
- Email: vorhauer@math.kent.edu
- Received by editor(s): May 18, 2001
- Published electronically: June 19, 2003
- Additional Notes: The first author was supported in part by NSF Grant DMS 0070720
- © Copyright 2003 American Mathematical Society
- Journal: Math. Comp. 73 (2004), 493-513
- MSC (2000): Primary 11B83, 11A63, 11Y70, 34J10
- DOI: https://doi.org/10.1090/S0025-5718-03-01513-8
- MathSciNet review: 2034134