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Triangular numbers and perfect squares

Published online by Cambridge University Press:  01 August 2016

Tom Beldon  and
Tony Gardiner
Tom Beldon
Affiliation:
50 Blakemere Road, Welwyn Garden City AL8 7PJ
Tony Gardiner
Affiliation:
77 Farquhar Road, Birmingham B15 2QP
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Extract

The nth triangular number is defined to be the sum of the first n positive integers:

Thus

In a letter to Mersenne in 1638 [1, p. 61], Fermat claimed that every positive integer can be written as a sum of at most three triangular numbers. This remarkable result was eventually proved by Gauss in 1796, at the age of 19.

Type
Articles
Information
The Mathematical Gazette , Volume 86 , Issue 507 , November 2002 , pp. 423 - 431
Copyright
Copyright © The Mathematical Association 2002

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References

1. Weil, A., Number theory: an approach though history; From Hammurapi to Legendre, Birkhäuser (1984).Google Scholar
2. Fauvel, J. and Gray, J., The history of mathematics: a reader, Macmillan (1987).Google Scholar
3. Gauss, C. F., Disquisitiones Arithmeticae (English edition), Springer-Verlag (1986).Google Scholar
4. Heath, T., A history of Greek mathematics (Vol. 1), Dover (1981).Google Scholar