English Title

On the resolution of formulas of squares of indeterminates by integral numbers

Authors

Leonhard Euler

Enestrom Number

279

Fuss Index

62

Original Language

Latin

Published as

Journal article

Published Date

1764

Written Date

1758

Archive Notes

According to Jacobi, a treatise with this title was read to the Berlin Academy on September 21, 1758. According to St. Petersburg Academy records, it was presented to that Academy on October 15, 1759.

Content Summary

In this paper, Euler returns to the equation axx+bx+c = yy, first approached in E29, and uses the tools of Pell's equation. He also discovers some of the properties of quadratic reciprocity. On the last page, he uses the phrase "Theory of Numbers," possibly the first use of this term.

Original Source Citation

Novi Commentarii academiae scientiarum Petropolitanae, Volume 9, pp. 3-39.

Opera Omnia Citation

Series 1, Volume 2, pp.576-611.

Record Created

2018-09-25

Included in

Mathematics Commons

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