English Title

On the resolution of irrationals by continued fractions, where a certain minor new and singular type is set forth

Authors

Leonhard Euler

Enestrom Number

454

Fuss Index

93

Original Language

Latin

Published as

Journal article

Published Date

1774

Written Date

1772

Content Summary

This paper begins with a review of Pell’s equation and continued fractions. It includes the following problems: (1) Given that the formula Ax2–2Bxy+Cy2 produces the value c when x=a and y=b, find an infinity of other values for x and y that produce that same value c, assuming that the quantity B2AC is a positive non-square number; (2) Given a formula Ax2Bxy+Cy2 in which B2AC is a positive non-square number, find values for x and y that produce the minimum value in this formula.

Original Source Citation

Novi Commentarii academiae scientiarum Petropolitanae, Volume 18, pp. 218-244.

Opera Omnia Citation

Series 1, Volume 3, pp.310-334.

Record Created

2018-09-25

Included in

Mathematics Commons

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