E515  De casibus quibusdam maxime memorabilibus in analysi indeterminata, ubi imprimis insignis usus calculi angulorum in analysi Diophantea ostenditur
(English Translation of Title)
Summary:
Euler returns to the problems of E253. Problem 1 is to find four rational numbers x, y, z, and v such that x^{4} + y^{4} + z^{4}  2xxyy  2xxzz  2yyzz + 2xxvv + 2yyvv + 2zzvv + v^{4} = 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.
Publication:

Originally published in Acta Academiae Scientarum Imperialis Petropolitinae 1778, 1781, pp. 85110

Opera Omnia: Series 1, Volume 3, pp. 429  452
 Reprinted in Commentat. arithm. 2, 1849, pp. 366379 [E515a]
Documents Available:
 Original Publication: E515
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