E255 -- Solutio generalis quorundam problematum Diophanteorum, quae vulgo nonnisi solutiones speciales admittere videntur
(General solution of certain Diophantine problems, which are ordinarily thought to admit only special solutions)
Summary:
In section 16, Euler finds all kinds of three cubes that have as their sum a cube. He shows the relationship to forms aa+3bb. In section 32, he looks at ways to find two relatively prime numbers that, when their cubes are added, makes a square. A footnote (p. 432) points us to the supplement to Heath’s Diophantus of Alexandria, containing "some solutions of Diophantine problems by Euler."
According to C. G. J. Jacobi, a treatise with this title was read to the Berlin Academy on May 9,
1754.
According to the records, it was presented to the St. Petersburg Academy on September 30,
1754.
Publication:
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Originally published in Novi Commentarii academiae scientiarum Petropolitanae 6, 1761, pp. 155-184
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Opera Omnia: Series 1, Volume 2, pp. 428 - 458
- Reprinted in Commentat. arithm. 1, 1849, pp. 193-209 [E255a]
Documents Available:
- Original publication: E255
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