Observations about two biquadratics, of which the sum is able to be resolved into two other biquadratics
(May 2005)

In this paper Euler considers the Diophantine equation A^4+B^4=C^4+D^4. He gives a method for finding solutions of it, and gives two particular solutions of A=2219449, B=-555617, C=1584749, D=2061283 and A=477069, B=8497, C=310319, D=428397; the first four satisfy this but the second four do not. Euler also states the ``Euler quartic conjecture'' in this paper, that there is no biquadratic which is the sum of three other biquadratics. However, this may be because of typographical errors or a bad digital copy of the original, and I will try to get a cleaner copy to double check.
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