English Title

New assistance for solving the formula axx + 1 = yy

Authors

Leonhard Euler

Enestrom Number

559

Fuss Index

64

Original Language

Latin

Published as

Collection article

Published Date

1783

Written Date

1773

Content Summary

This describes Euler's solution of the Pell equation without the use of continued fractions. It opens with a big one: if a=61, then x=226,153,980 and y=1,766,319,049. Euler includes the following problems: Knowing a solution to app−1=qq, find numbers x and y that make axx+1=yy; i.e., find a relationship between the positive equation and the negative equation. Then, knowing app−2=qq, solve axx+1=yy.

Original Source Citation

Opuscula analytica, Volume 1, pp. 329-344.

Opera Omnia Citation

Series 1, Volume 4, pp.76-90.

Record Created

2018-09-25

Included in

Mathematics Commons

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