Theorematum quorundam arithmeticorum demonstrationes

2012/02/16 by Leonhard Euler, Euler, Leonhard, Artur Diener +3
Mathematics · Social Sciences · #FOS: Mathematics #Historical and Literary Studies #History and Overview (math.HO) #History and Theory of Mathematics #Mathematics and Applications #math.HO

paper · pdf · doi:10.48550/arxiv.1202.3808

arxiv created 2012/02/16 · openalex publication_date 2012/02/16 · arxiv updated 2012/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Euler proves that the sum of two 4th powers can't be a 4th power and that the difference of two distinct non-zero 4th powers can't be a 4th power and Fermat's theorem that the equation x(x+1)/2=y⁴ can only be solved in integers if x=1 and the final theorem y³+1=x² can only be solves for x=3 and y=2 in integers. The paper is translated from Euler's Latin original into German.

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