English Title

An easy rule for Diophantine problems which are to be resolved quickly by integral numbers

Authors

Leonhard Euler

Enestrom Number

739

Fuss Index

79

Original Language

Latin

Published as

Journal article

Published Date

1813

Written Date

1778

Content Summary

Euler returns to the problem of making formulas of the form axx+bx+g into squares. He generalizes to try to find a and b solving axx+bx+g = zyy+hy+t. This seems to rely on an initial solution and a clever application of solutions to Pell’s equation.

He does some nice examples: (1) find all triangular numbers that are also squares, (2) find all square numbers that, diminshed by one, are triangular numbers, (3) find those triangular numbers that, when tripled, are again triangular numbers.

Original Source Citation

Mémoires de l'académie des sciences de St.-Petersbourg, Volume 4, pp. 3-17.

Opera Omnia Citation

Series 1, Volume 4, pp.406-417.

Record Created

2018-09-25

Included in

Mathematics Commons

Share

COinS