#### English Title

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

#### 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