E763 -- De tribus pluribusve numeris inveniendis, quorum summa sit quadratum, quadratorum vero summa biquadratum
(English Translation of Title)
Summary:
Euler attributes this problem to Fermat and says he got it from Lagrange, to find three numbers, x, y, and z
such that x + y + z is a square and xx + yy + zz is a fourth power. He starts with a 2-variable problem,
asking that x + y be square and xx + yy a fourth power. He finds a pair of numbers in the trillions.
Then he finds a 3-variable solution, x = 49, y = 64, z = 8 and goes on to four variables,
x = 193, y = 104, z = 48, v = 16 and even five variables.
Publication:
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Originally published in Memoires de l'academie des sciences de St.-Petersbourg 9, 1824, pp. 3-13
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Opera Omnia: Series 1, Volume 5, pp. 61 - 70
- Reprinted in Commentat. arithm. 2, 1849, pp. 397-402 [E763a]
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