English Title

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

Authors

Leonhard Euler

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

Included in

Mathematics Commons

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