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Sums of powers of integers – how Fermat may have found them

Published online by Cambridge University Press:  23 January 2015

Bob Burn
Bob Burn*
Affiliation:
Sunnyside, Barrack Road, Exeter EX2 6AB, e-mail: R.P.Burn@exeter.ac.uk
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Extract

On 22 September 1636, Fermat wrote to Roberval, [I, FO.II.XIII, p.71], saying that he had found the quadrature of an infinite number of curves. He named in particular the ‘solid parabola’, y = x3 , and said that his method was different from Archimedes‘ quadrature of the parabola. He invited Roberval to share his thoughts on this and other matters.

On 11th October 1636, Roberval replied to Fermat [1. FO.II.XIV, p.75], indicating his method for determining the quadrature of the ‘solid parabola’ and extending it to the quadrature of y = x4 and y = x5 .

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Type
Articles
Information
The Mathematical Gazette , Volume 94 , Issue 529 , March 2010 , pp. 18 - 26
Copyright
Copyright © The Mathematical Association 2010

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References

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