English Title

Example of the use of observation in pure mathematics

Authors

Leonhard Euler

Enestrom Number

256

Fuss Index

4

Original Language

Latin

Published as

Journal article

Published Date

1761

Written Date

1754

Archive Notes

According to Jacobi, a treatise with this title was read to the Berlin Academy on November 22, 1753. According to St. Petersburg Academy records, it was presented to that Academy on September 30, 1754.

Content Summary

Euler attempts to explain his thought process by working out problems in quadratic forms in great detail. Euler notes that numbers of the form 2aa + bb are closed under multiplication. He develops more properties of such numbers and proves some of them. Then he uses these properties to show that 67579 = 2∙872+2292 is prime, while 40081 is not.

Original Source Citation

Novi Commentarii academiae scientiarum Petropolitanae, Volume 6, pp. 185-230.

Opera Omnia Citation

Series 1, Volume 2, pp.459-492.

Record Created

2018-09-25

Included in

Mathematics Commons

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