odd number theorem is a theorem in strong gravitational lensing which comes directly from differential topology. The theorem states that the number of...

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...

In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers a, b,...

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...

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...

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...

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...

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...

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...

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...

The hairy ball theorem of algebraic topology (sometimes called the hedgehog theorem in Europe) states that there is no nonvanishing continuous tangent...

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...

Lovelock's theorem (physics) No-hair theorem (physics) Odd number theorem (physics) Peeling theorem (physics) Penrose–Hawking singularity theorems (physics)...

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...

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...

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...

In number theory, Chen's theorem states that every sufficiently large even number can be written as the sum of either two primes or a prime and a semiprime...

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...

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...

In mathematics, Euler's pentagonal number theorem relates the product and series representations of the Euler function. It states that ∏ n = 1 ∞ ( 1 −...

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...

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...

In topology, the Jordan curve theorem (JCT), formulated by Camille Jordan in 1887, asserts that every Jordan curve (a plane simple closed curve) divides...

Jacobi's theorem can refer to: Maximum power theorem, in electrical engineering The result that the determinant of skew-symmetric matrices with odd size vanishes...

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...

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...

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...

rings. Topologically, multiple image production is governed by the odd number theorem. Strong lensing was predicted by Albert Einstein's general theory...

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...

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...