On the cases in which the form x4 + kxxyy + y4 can be reduced to a square
Euler first notes that if the values 1, 3, 4, 5, 6, 7, etc. are substituted for k, then the formula x4 + kxxyy + y4 never gives a square, regardless of the values x and y. He repeats several of his results about Pell's equation.
Original Source Citation
Nova Acta Academiae Scientiarum Imperialis Petropolitanae, Volume 10, pp. 27-40.
Opera Omnia Citation
Series 1, Volume 4, pp.235-244.