English Title

New demonstrations about the divisors of numbers of the form xx + nyy

Authors

Leonhard Euler

Enestrom Number

610

Fuss Index

15

Original Language

Latin

Published as

Journal article

Published Date

1787

Written Date

1775

Content Summary

First, Euler presents some familiar theorems about quadratic residues. Then he presents two main theorems: If n is of the form 4k+1 or 4k+2, then the only prime divisors of xx+nyy are of the form 4ni+2n−1; and If n is of the form 4k or 4k−1, then the only prime divisors of xx+nyy are of the form 4ni−2n+1.

Original Source Citation

Nova Acta Academiae Scientiarum Imperialis Petropolitanae, Volume 1, pp. 47-74.

Opera Omnia Citation

Series 1, Volume 4, pp.197-220.

Record Created

2018-09-25

Included in

Mathematics Commons

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