General solution of certain Diophantine problems, which are ordinarily thought to admit only special solutions
The supplement to T. L. Heath's Diophantus of Alexandria, contains a section titled "some solutions of Diophantine problems by Euler," which includes some of Euler's work in this paper. According to Jacobi, a treatise with this title was read to the Berlin Academy on May 9, 1754. According to St. Petersburg Academy records, it was presented to that Academy on September 30, 1754.
In section 16, Euler finds several sets of three cubes whose sum is a cube. He shows the relationship to forms aa+3bb. In section 32, he shows how to find two relatively prime numbers that, when their cubes are added, make a square.
Original Source Citation
Novi Commentarii academiae scientiarum Petropolitanae, Volume 6, pp. 155-184.
Opera Omnia Citation
Series 1, Volume 2, pp.428-458.