De divisoribus numerorum in forma mxx+nyy contentorum

English Title

On divisors of numbers of the form mxx + nyy

Authors

Leonhard Euler

Enestrom Number

744

Fuss Index

14

Original Language

Latin

Content Summary

First, Euler notes that divisors of xx+yy (x and y relatively prime) must be of the form 4N+1, then that divisors of 2xx+yy must be of the form 8N+1 or 8N+3, and those of 3xx+yy are of the form 12N+1 or 12N+7. He generalizes this result by analyzing the divisors of mxx+nyy. Interestingly, one can state the congruence classes modulo 4mn which hold divisors of mxx+nyy once one knows the value of the product mn, regardless of the particular values of m and n. Euler presents a table of congruence classes modulo 4mn holding divisors of mxx+nyy for small values of mn.

Published as

Journal article

Published Date

1815

Written Date

1778

Original Source Citation

Mémoires de l'académie des sciences de St.-Petersbourg, Volume 5, pp. 3-23.

Opera Omnia Citation

Series 1, Volume 4, pp.418-431.

Record Created

2018-09-25