✦ LIBER ✦

On Euler's contributions to the four-squares theorem

✍ Scribed by Herbert Pieper

Publisher: Elsevier Science
Year: 1993
Tongue: English
Weight: 361 KB
Volume: 20
Category: Article
ISSN: 0315-0860
DOI: 10.1006/hmat.1993.1003

No coin nor oath required. For personal study only.

✦ Synopsis

A passage in Euler's notebook 132 (written between 1740 and 1744) concerning the foursquares theorem is interpreted in a new way. The proof of the four-squares theorem is based on three lemmas. Euler proved two of them from which he deduced the theorem on the representation as a sum of four squares of fractions. But Euler was not able to prove the third lemma though it is formulated in notebook 132.

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