Authors

Leonhard Euler

Enestrom Number

702

Fuss Index

42

Original Language

Latin

Published as

Journal article

Published Date

1798

Written Date

1777

Content Summary

Euler searches for all integers N such that the formulas A2+B2 and A2+NB2 can both be squares at the same time. By putting A = xxyy and B = 2xy, the first expression becomes a square; to make the other one a square also, one takes the A2 to be zz and obtains (x+y)/z ± xx/(zz), and the question reduces to finding values for z such that N becomes an integer. He finds, among the first 100 natural numbers, the following values for N that satisfy the problem: 7, 10, 11, 17, ....

Original Source Citation

Nova Acta Academiae Scientiarum Imperialis Petropolitanae, Volume 11, pp. 78-93.

Opera Omnia Citation

Series 1, Volume 4, pp.255-268.

Record Created

2018-09-25

Included in

Mathematics Commons

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