E776 -- Dilucidationes circa binas summas duorum biquadratorum inter se aequales
(Elucidations about two sums of pairs of biquadratics, which are mutually equal)
Summary:
Euler shows that A4 + B4 = C4 + D4 for
A = 477069, B = 8497, C = 310319, D = 428397 and for some other sets of values.
Publication:
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Originally published in Memoires de l'academie des sciences de St.-Petersbourg 11, 1830, pp. 49-57
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Opera Omnia: Series 1, Volume 5, pp. 135 - 145
- Reprinted in Commentat. arithm. 2, 1849, pp. 450-456 [E776a]
Documents Available:
- Original publication: E776
- The Euler Archive attempts to monitor current scholarship for articles and books that may be of interest to Euler Scholars. Selected references we have found that discuss or cite E776 include:
- Lander LJ., “Geometric aspects of Diophantine equations involving equal sums of like powers.” American Mathematical Monthly, 75 (10), pp. 1061-& (1968).
- Zajta AJ., “Solutions of the Diophantine equation A4 + B4 = C4 + D4.” Mathematics of Computation, 41 (164), pp. 635-659 (1983).
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