E515 -- De casibus quibusdam maxime memorabilibus in analysi indeterminata, ubi imprimis insignis usus calculi angulorum in analysi Diophantea ostenditur
(English Translation of Title)
Euler returns to the problems of E253. Problem 1 is to find four rational numbers x, y, z, and v such that x4 + y4 + z4 - 2xxyy - 2xxzz - 2yyzz + 2xxvv + 2yyvv + 2zzvv + v4 = 0. He finds several solutions, the first being x = 39, v = 12, y = 20, and z = 25.
According to the
records, it was presented to the St. Petersburg Academy on May 1, 1780.
Originally published in Acta Academiae Scientarum Imperialis Petropolitinae 1778, 1781, pp. 85-110
Opera Omnia: Series 1, Volume 3, pp. 429 - 452
- Reprinted in Commentat. arithm. 2, 1849, pp. 366-379 [E515a]
- Original Publication: E515
Return to the Euler Archive