The proofs of some arithmetic theorems
According to Eneström, additions to this work were presented to the St. Petersburg Academy on 16 August 1738.
Euler proves that the sum of two 4th powers can't be a 4th power, that the difference of two distinct non-zero 4th powers can't be a 4th power, and other such forms.
Original Source Citation
Commentarii academiae scientiarum Petropolitanae, Volume 10, pp. 125-146.
Opera Omnia Citation
Series 1, Volume 2, pp.38-58.