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x4 + dx2y2 + y2= z2: Some cases with only trivial solutions—and a solution Euler missed
Published online by Cambridge University Press: 18 May 2009
Extract
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 d = 85 (a case Euler missed). With these results, the question of whether
has nontrivial solutions is now answered for all d, 0≤d ≤100.
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- Copyright © Glasgow Mathematical Journal Trust 1989
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