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.

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