E758 -- De binis formulis speciei xx + myy et xx + nyy inter se concordibus et discordibus
(English Translation of Title)
Summary:
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.
Publication:
-
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]
Documents Available:
- Original publication: E758
Return to the Euler Archive