E696  De casibus quibus hanc formulam x^{4} + kxxyy + y^{4} ad quadratum reducere licet
(On the cases in which the form x^{4} + kxxyy + y^{4} is permitted to be reduced to a square)
Summary:
Euler first notes that if the values 1, 3, 4, 5, 6, 7, etc. are substituted for k, then the formula never gives a square, regardless of the values x and y. He repeats several of his results about Pell's equation.
Publication:

Originally published in Nova Acta Academiae Scientarum Imperialis Petropolitinae 10, 1797, pp. 2740

Opera Omnia: Series 1, Volume 4, pp. 235  244
 Reprinted in Commentat. arithm. 2, 1849, pp. 183189 [E696a]
Documents Available:
 Original Publication: E696
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