English Title

An investigation of two numbers of the form xy(x4y4), of which the product and the quotient will be a square

Authors

Leonhard Euler

Enestrom Number

774

Fuss Index

48

Original Language

Latin

Published as

Journal article

Published Date

1830

Written Date

1780

Content Summary

In Volume XV of the Novi Commentarii, Euler found integers x, y, z such that xy±z(x+y) and xy±z(xy) are all squares. In this paper, he describes a more elegant solution, which first requires one to determine when xy(x4y4) is a square. Then, given an initial solution, he uses a double-quadratic technique to find a chain of solutions.

Original Source Citation

Mémoires de l'académie des sciences de St.-Petersbourg, Volume 11, pp. 31-45.

Opera Omnia Citation

Series 1, Volume 5, pp.116-130.

Record Created

2018-09-25

Included in

Mathematics Commons

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