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, while xx+yy and xx+7yy are concordant (e.g., x=3, y=4). Euler seems to get partial results.
Original Source Citation
Mémoires de l'académie des sciences de St.-Petersbourg, Volume 8, pp. 3-16.
Opera Omnia Citation
Series 1, Volume 5, pp.48-60.