@article{Euler2012TheorematumQA,
title={Theorematum quorundam arithmeticorum demonstrationes},
author={Leonhard Euler and A. Diener and Alexander Aycock},
journal={arXiv: History and Overview},
year={2012}
}

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=y^4 can only be solved in integers if x=1 and the final theorem y^3+1=x^2 can only be solves for x=3 and y=2 in integers. The paper is translated from Euler's Latin original into German.