E270 -- Solutio problematis de investigatione trium numerorum, quorum tam summa quam productum nec non summa productorum ex binis sint numeri quadrati
( The solution of a problem about searching for three numbers, of which the sum and not only their product but the sum of their products two apiece, are square numbers.)
Summary:
Euler wants to make the following three numbers all be squares: n(x + y + z), nn(xy + xz + yz) and n3xyz. He doesn’t say why he wants these to be squares. His first solution is x = 3/2, y = 4/3, and z = 17/6. Then n = 6(34).
According
to C. G. J. Jacobi, a treatise with almost the same title appears to have been read to the Berlin
Academy on February 27, 1755.
According to the records, it was presented to the St. Petersburg
Academy on March 8, 1756.
Publication:
-
Originally published in Novi Commentarii academiae scientiarum Petropolitanae 8, 1763, pp. 64-73
-
Opera Omnia: Series 1, Volume 2, pp. 519 - 530
- Reprinted in Commentat. arithm. 1, 1849, pp. 239-244 [E270a]
- A handwritten French translation of this treatise can be found in the library of the observatory in
Uccle, near Brussels.
Documents Available:
- Original publication: E270
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