E758 -- De binis formulis speciei xx + myy et xx + nyy inter se concordibus et discordibus
(English Translation of Title)
Two forms are called concordant if there exist values of x and y that make both forms into squares at the same time.
If they are not concordant, they are called discordant. For example, xx + yy and xx - yy are discordant,
and xx + yy and xx + 7yy are concordant (e.g. x = 3, y = 4). Euler seems to get partial results.
Originally published in Memoires de l'academie des sciences de St.-Petersbourg 8, 1822, pp. 3-16
Opera Omnia: Series 1, Volume 5, pp. 48 - 60
- Reprinted in Commentat. arithm. 2, 1849, pp. 406-413 [E758a]
- Original publication: E758
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