Fermat's Theorem (stationary Points), Fermat's Theorem
   HOME

TheInfoList



OR:

The works of the 17th-century mathematician
Pierre de Fermat Pierre de Fermat (; ; 17 August 1601 – 12 January 1665) was a French mathematician who is given credit for early developments that led to infinitesimal calculus, including his technique of adequality. In particular, he is recognized for his d ...
engendered many
theorem In mathematics and formal logic, a theorem is a statement (logic), statement that has been Mathematical proof, proven, or can be proven. The ''proof'' of a theorem is a logical argument that uses the inference rules of a deductive system to esta ...
s. Fermat's theorem may refer to one of the following theorems: *
Fermat's Last Theorem In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive number, positive integers , , and satisfy the equation for any integer value of greater than . The cases ...
, about integer solutions to ''a''''n'' + ''b''''n'' = ''c''''n'' *
Fermat's little theorem In number theory, Fermat's little theorem states that if is a prime number, then for any integer , the number is an integer multiple of . In the notation of modular arithmetic, this is expressed as a^p \equiv a \pmod p. For example, if and , t ...
, a property of prime numbers *
Fermat's theorem on sums of two squares In additive number theory, Pierre de Fermat, Fermat's theorem on sums of two squares states that an Even and odd numbers, odd prime number, prime ''p'' can be expressed as: :p = x^2 + y^2, with ''x'' and ''y'' integers, if and only if :p \equiv ...
, about primes expressible as a sum of squares *
Fermat's theorem (stationary points) In mathematics, the interior extremum theorem, also known as Fermat's theorem, is a theorem which states that at the local extrema of a differentiable function, its derivative is always zero. It belongs to the mathematical field of real analysis ...
, about local maxima and minima of differentiable functions *
Fermat's principle Fermat's principle, also known as the principle of least time, is the link between geometrical optics, ray optics and physical optics, wave optics. Fermat's principle states that the path taken by a Ray (optics), ray between two given ...
, about the path taken by a ray of light *
Fermat polygonal number theorem In additive number theory, the Fermat polygonal number theorem states that every positive integer is a sum of at most -gonal numbers. That is, every positive integer can be written as the sum of three or fewer triangular numbers, and as the sum ...
, about expressing integers as a sum of polygonal numbers *
Fermat's right triangle theorem Fermat's right triangle theorem is a non-existence mathematical proof, proof in number theory, published in 1670 among the works of Pierre de Fermat, soon after his death. It is the only complete proof given by Fermat. It has many equivalent for ...
, about squares not being expressible as the difference of two fourth powers


See also

*
List of things named after Pierre de Fermat This is a list of things named after Pierre de Fermat, a French amateur mathematician. * Fermat–Apollonius circle *Fermat–Catalan conjecture *Fermat cubic *Fermat curve * Fermat–Euler theorem *Fermat number * Fermat point * Fermat–Weber pr ...
{{SIA Set index articles on mathematics