English Title

General solution of certain Diophantine problems, which are ordinarily thought to admit only special solutions

Authors

Leonhard Euler

Enestrom Number

255

Fuss Index

73

Original Language

Latin

Published as

Journal article

Published Date

1761

Written Date

1754

Archive Notes

The supplement to T. L. Heath's Diophantus of Alexandria, contains a section titled "some solutions of Diophantine problems by Euler," which includes some of Euler's work in this paper. According to Jacobi, a treatise with this title was read to the Berlin Academy on May 9, 1754. According to St. Petersburg Academy records, it was presented to that Academy on September 30, 1754.

Content Summary

In section 16, Euler finds several sets of three cubes whose sum is a cube. He shows the relationship to forms aa+3bb. In section 32, he shows how to find two relatively prime numbers that, when their cubes are added, make a square.

Original Source Citation

Novi Commentarii academiae scientiarum Petropolitanae, Volume 6, pp. 155-184.

Opera Omnia Citation

Series 1, Volume 2, pp.428-458.

Record Created

2018-09-25

Included in

Mathematics Commons

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