Infinitely many quartic rational Diophantine quadruples exist and are parametrized by rational points on the Euler surface X^4 + Y^4 = Z^4 + W^4.
Bremner, On the quartic surfacex4 +y4 = z4 +w4,Acta Arith.220(2025), no
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Quartic Rational Diophantine Quadruples and the Euler Surface
Infinitely many quartic rational Diophantine quadruples exist and are parametrized by rational points on the Euler surface X^4 + Y^4 = Z^4 + W^4.