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<i>x</i><sup>4</sup> + <i>dx</i><sup>2</sup><i>y</i><sup>2</sup> + <i>y</i><sup>2</sup>= <i>z</i><sup>2</sup>: Some cases with only trivial solutions—and a solution Euler missed
Mathematicians have studied the diophantine equation of the title ever since the days of Fermat, Leibniz and Euler. In this paper, we review the history of this problem, present several new classes of values of d for which the equation has only trivial solutions, and find a nontrivial solution for …