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Triangular numbers and perfect squares
Published online by Cambridge University Press: 01 August 2016
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.
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