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%I #6 Mar 30 2012 16:45:26
%S 90239171293339457,43217672330080936976,6822171645549542113537,
%T 497455247066570553051152,20549128177340906621890817,
%U 24223393095189686902587392,549140647573975773898200592
%N Euler's family of solutions to n = x^4 + y^4 = z^4 + w^4.
%D Mordell, Diophantine Equations, 1969, p. 90.
%p Set x := a^7+a^5*b^2-2*a^3*b^4+3*a^2*b^5+a*b^6; y := a^6*b-3*a^5*b^2-2*a^4*b^3+a^2*b^5+b^7; z := a^7+a^5*b^2-2*a^3*b^4-3*a^2*b^5+a*b^6; w := a^6*b+3*a^5*b^2-2*a^4*b^3+a^2*b^5+b^7; then x^4+y^4=z^4+w^4.
%Y Cf. A003824.
%K nonn
%O 1,1
%A _N. J. A. Sloane_.