English Title
Observations about two biquadratics, of which the sum is able to be resolved into two other biquadratics
Enestrom Number
428
Fuss Index
67
Original Language
Latin
Content Summary
Euler considers solutions to A4+B4 = C4+D4 and gives a method for finding solutions. Using this method, he finds the solutions (A, B, C, D) = (2219449, -555617, 1584749, 2061283) and (477069, 8497, 310319, 428397); the first set of numbers satisfies the equation, but the second does not. He also states the "Euler quartic conjecture," which claims that there is no biquadratic that is equal to the sum of three other biquadratics. (Based on Jordan Bell's translation abstract.)
Published as
Journal article
Published Date
1773
Written Date
1772
Original Source Citation
Novi Commentarii academiae scientiarum Petropolitanae, Volume 17, pp. 64-69.
Opera Omnia Citation
Series 1, Volume 3, pp.211-217.
Record Created
2018-09-25
E428en.pdf (87 kB)
