E428 -- Observationes circa bina biquadrata, quorum summam in duo alia biquadrata resolvere liceat

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

(based on Jordan Bell's abstract)
Euler considers solutions to A4 + B4 = C4 + D4 and gives a method for finding solutions. Using this method he finds the solutions A = 2219449, B = -555617, C = 1584749, D = 2061283 and A = 477069, B = 8497, C = 310319, D=428397; the first four numbers satisfy the equation, but the second four do not. He also states the "Euler quartic conjecture," which says that there is no biquadratic that is the sum of three other biquadratics.

According to the records, it was presented to the St. Petersburg Academy on January 13, 1772.

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