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...

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...

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

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...

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...

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...

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...

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...

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 number theory, Dirichlet's theorem, also called the Dirichlet prime number theorem, states that for any two positive coprime integers a and d, there...

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 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...

Theorem is a theorem in number theory, originally stated by Pierre de Fermat in 1637 and proven by Andrew Wiles in 1995. The statement of the theorem...

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...

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

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...

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...

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...

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...

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...

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, 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...

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...

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...

graph, the number of vertices that touch an odd number of edges is even. For example, if there is a party of people who shake hands, the number of people...