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The theorem plays a key role in the 1948 mystery novel Murder by Mathematics by Hector Hawton. [1] [2]Arthur Porges' short story "The Devil and Simon Flagg" features a mathematician who bargains with the Devil that the latter cannot produce a proof of Fermat's Last Theorem within twenty-four hours. [3]
Math Girls (数学ガール, Sūgaku gāru) is the first in a series of math-themed young adult novels of the same name by Japanese author Hiroshi Yuki. It was published by SoftBank Creative in 2007, followed by Math Girls: Fermat's Last Theorem in 2008, Math Girls: Gödel's Incompleteness Theorems in 2009, and Math Girls: Randomized Algorithms in 2011.
In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers a, b, and c satisfy the equation a n + b n = c n for any integer value of n greater than 2. The cases n = 1 and n = 2 have been known since antiquity to have infinitely many solutions. [1]
If a is not divisible by p, that is, if a is coprime to p, then Fermat's little theorem is equivalent to the statement that a p − 1 − 1 is an integer multiple of p, or in symbols: [1] [2] (). For example, if a = 2 and p = 7 , then 2 6 = 64 , and 64 − 1 = 63 = 7 × 9 is a multiple of 7 .
Fermat's theorem is central to the calculus method of determining maxima and minima: in one dimension, one can find extrema by simply computing the stationary points (by computing the zeros of the derivative), the non-differentiable points, and the boundary points, and then investigating this set to determine the extrema.
Fermat's Last Theorem states that no three positive integers (a, b, c) can satisfy the equation a n + b n = c n for any integer value of n greater than 2. (For n equal to 1, the equation is a linear equation and has a solution for every possible a and b.
In mathematics, a proof by infinite descent, also known as Fermat's method of descent, is a particular kind of proof by contradiction [1] used to show that a statement cannot possibly hold for any number, by showing that if the statement were to hold for a number, then the same would be true for a smaller number, leading to an infinite descent and ultimately a contradiction. [2]
There are infinitely many Fermat pseudoprimes to any given basis a > 1. [1]: Theorem 1 Even worse, there are infinitely many Carmichael numbers. [2] These are numbers for which all values of with (,) = are Fermat liars. For these numbers, repeated application of the Fermat primality test performs the same as a simple random search for factors.