• odd number theorem is a theorem in strong gravitational lensing which comes directly from differential topology. The theorem states that the number of...
    5 KB (635 words) - 07:56, 22 June 2024
  • Thumbnail for Prime number
    smaller than 4. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime...
    117 KB (14,179 words) - 14:11, 24 March 2025
  • In mathematics, the Feit–Thompson theorem, or odd order theorem, states that every finite group of odd order is solvable. It was proved in the early 1960s...
    22 KB (2,958 words) - 06:27, 19 March 2025
  • Thumbnail for 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 integers a, b,...
    103 KB (11,494 words) - 07:52, 21 March 2025
  • Thumbnail for Parity (mathematics)
    The Feit–Thompson theorem states that a finite group is always solvable if its order is an odd number. This is an example of odd numbers playing a role...
    21 KB (2,528 words) - 17:29, 19 March 2025
  • Thumbnail for Brooks' theorem
    odd length, which require Δ + 1 colors. The theorem is named after R. Leonard Brooks, who published a proof of it in 1941. A coloring with the number...
    8 KB (929 words) - 05:27, 1 December 2024
  • In number theory, Fermat's little theorem states that if p is a prime number, then for any integer a, the number ap − a is an integer multiple of p. In...
    18 KB (2,368 words) - 00:07, 4 April 2025
  • Thumbnail for Classification of finite simple groups
    Groups of 2-rank 0, in other words groups of odd order, which are all solvable by the Feit–Thompson theorem. Groups of 2-rank 1. The Sylow 2-subgroups are...
    44 KB (3,991 words) - 20:20, 3 January 2025
  • The fundamental theorem of algebra, also called d'Alembert's theorem or the d'Alembert–Gauss theorem, states that every non-constant single-variable polynomial...
    51 KB (7,621 words) - 23:44, 2 April 2025
  • Lovelock's theorem (physics) No-hair theorem (physics) Odd number theorem (physics) Peeling theorem (physics) Penrose–Hawking singularity theorems (physics)...
    78 KB (6,289 words) - 04:18, 18 March 2025
  • Thumbnail for Perfect number
    are of this form. This is known as the Euclid–Euler theorem. It is not known whether there are any odd perfect numbers, nor whether infinitely many perfect...
    38 KB (5,168 words) - 12:07, 29 March 2025
  • Thumbnail for Hairy ball theorem
    The hairy ball theorem of algebraic topology (sometimes called the hedgehog theorem in Europe) states that there is no nonvanishing continuous tangent...
    14 KB (1,809 words) - 08:56, 20 March 2025
  • In number theory, Dirichlet's theorem, also called the Dirichlet prime number theorem, states that for any two positive coprime integers a and d, there...
    24 KB (3,526 words) - 14:42, 11 January 2025
  • Thumbnail for Furry's theorem
    electrodynamics, Furry's theorem states that if a Feynman diagram consists of a closed loop of fermion lines with an odd number of vertices, its contribution...
    10 KB (1,223 words) - 20:58, 20 May 2024
  • In mathematics, Euler's pentagonal number theorem relates the product and series representations of the Euler function. It states that ∏ n = 1 ∞ ( 1 −...
    14 KB (2,118 words) - 00:38, 3 March 2025
  • Thumbnail for Lagrange's four-square theorem
    m is even or odd do not require separate arguments. The classical proof It is sufficient to prove the theorem for every odd prime number p. This immediately...
    25 KB (4,264 words) - 07:50, 24 February 2025
  • The Euclid–Euler theorem is a theorem in number theory that relates perfect numbers to Mersenne primes. It states that an even number is perfect if and...
    11 KB (1,409 words) - 11:32, 24 March 2025
  • In algebra and number theory, Wilson's theorem states that a natural number n > 1 is a prime number if and only if the product of all the positive integers...
    17 KB (2,306 words) - 00:58, 30 March 2025
  • In number theory, Vinogradov's theorem is a result which implies that any sufficiently large odd integer can be written as a sum of three prime numbers...
    6 KB (1,128 words) - 09:59, 1 November 2023
  • of this theorem applies to any finite number of colours, rather than just two. More precisely, the theorem states that for any given number of colours...
    66 KB (8,506 words) - 16:31, 3 April 2025
  • Thumbnail for Strong gravitational lensing
    rings. Topologically, multiple image production is governed by the odd number theorem. Strong lensing was predicted by Albert Einstein's general theory...
    6 KB (672 words) - 12:56, 29 January 2025
  • Thumbnail for Sum of two squares theorem
    In number theory, the sum of two squares theorem relates the prime decomposition of any integer n > 1 to whether it can be written as a sum of two squares...
    6 KB (835 words) - 10:50, 5 January 2025
  • perfect graph theorem is a forbidden graph characterization of the perfect graphs as being exactly the graphs that have neither odd holes (odd-length induced...
    15 KB (1,769 words) - 23:06, 16 October 2024
  • x p + y p = z p {\displaystyle x^{p}+y^{p}=z^{p}} of Fermat's Last Theorem for odd prime p {\displaystyle p} . Specifically, Sophie Germain proved that...
    3 KB (437 words) - 09:46, 24 February 2025
  • In number theory, Jacobi's four-square theorem gives a formula for the number of ways that a given positive integer n can be represented as the sum of...
    5 KB (673 words) - 11:28, 5 January 2025
  • (known as the Dottie number) is approximately x = 0.73908513321516 (thus x = cos(x) for this value of x). The Lefschetz fixed-point theorem (and the Nielsen...
    11 KB (1,278 words) - 00:51, 3 February 2024
  • Thumbnail for Squared triangular number
    proofs. A similar result to Nicomachus's theorem holds for all power sums, namely that odd power sums (sums of odd powers) are a polynomial in triangular...
    14 KB (1,867 words) - 19:23, 16 February 2025
  • In additive number theory, the Fermat polygonal number theorem states that every positive integer is a sum of at most n n-gonal numbers. That is, every...
    4 KB (434 words) - 20:22, 17 April 2023
  • In geometry, Monsky's theorem states that it is not possible to dissect a square into an odd number of triangles of equal area. In other words, a square...
    6 KB (620 words) - 03:33, 23 March 2025
  • Thumbnail for Bipartite graph
    graph theorem. It follows that any subgraph of a bipartite graph is also bipartite because it cannot gain an odd cycle. For a vertex, the number of adjacent...
    33 KB (4,093 words) - 00:09, 21 October 2024