caa a22 4500 386372179 CHVBK 20180307112001.0 cr unu---uuuuu 161130e198909 xx s 000 0 eng 10.1017/S0017089500007862 doi S0017089500007862 pii (NATIONALLICENCE)cambridge-10.1017/S0017089500007862 Brown Ezra Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061 x4 + dx2y2 + y2= z2: Some cases with only trivial solutions—and a solution Euler missed [Elektronische Daten] [Ezra Brown] 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. Copyright © Glasgow Mathematical Journal Trust 1989 Glasgow Mathematical Journal Cambridge University Press 31/3(1989-09), 297-307 0017-0895 31:3<297 1989 31 GMJ https://doi.org/10.1017/S0017089500007862 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0017089500007862 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Brown Ezra Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061 NATIONALLICENCE 773 0- Glasgow Mathematical Journal Cambridge University Press 31/3(1989-09), 297-307 0017-0895 31:3<297 1989 31 GMJ CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge