| Fermat also investigated maxima and minima by considering when the tangent to the curve was parallel to the x-axis. |
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| His favourite topics in number theory included binary quadratic forms, quadratic residues, Gauss sums and Fermat quotients. |
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| Fermat subsequently died, leaving mathematicians to search for 350 years for a proof of the theorem. |
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| Fermat preferred the algebraic techniques that he used to such devastating effect in number theory. |
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| Fermat proposed that light follows the path which takes the shortest time, enabling Snell's law of refraction to be deduced mathematically. |
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| It could be hoped that this Fermat test would give an if and only if test for primeness. |
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| This work contained the first known method of elimination and Fermat wanted it published. |
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| Fermat had asked for a cube n such that the sum of the divisors of n is a square, and a square n such that the sum of the divisors of n is a cube. |
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| His textbook for graduate and undergraduate courses in number and Galois theory covers from Fermat to Gauss, class field theory, complex multiplication, and additional topics. |
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| Pierre de Fermat, claiming that he borrowed from Diophantus, introduced the concept of adequality, which represented equality up to an infinitesimal error term. |
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