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New demonstrations about the resolution of numbers into squares

2008/05/31 by Leonhard Euler, Euler, Leonhard
Computer Science · Mathematics · #01A50 #11-03 #11E25 #Computability, Logic, AI Algorithms #FOS: Mathematics #History and Overview (math.HO) #History and Theory of Mathematics #Number Theory (math.NT) #math.HO #math.NT #msc:01A50 #msc:11-03 #msc:11E25

paper · pdf · doi:10.48550/arxiv.0806.0104

19 pages

arxiv created 2008/05/31 · openalex publication_date 2008/05/31 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Translated from the Latin original "Novae demonstrationes circa resolutionem numerorum in quadrata" (1774). E445 in the Enestrom index. See Chapter III, section XI of Weil's "Number theory: an approach through history". Also, a very clear proof of the four squares theorem based on Euler's is Theorem 370 in Hardy and Wright, "An introduction to the theory of numbers", fifth ed. It uses Theorem 87 in Hardy and Wright, but otherwise does not assume anything else from their book. I translated most of the paper and checked those details a few months ago, but only finished last few parts now. If anything isn't clear please email me.

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