In the mathematical discipline of graph theory, the 2-factor theorem, discovered by Julius Petersen, is one of the earliest works in graph theory. It can...

In algebra, the factor theorem connects polynomial factors with polynomial roots. Specifically, if f ( x ) {\displaystyle f(x)} is a polynomial, then x...

linear factor) of Gauss's lemma on the factorization of polynomials. The integral root theorem is the special case of the rational root theorem when the...

Stolper–Samuelson theorem is a theorem in Heckscher–Ohlin trade theory. It describes the relationship between relative prices of output and relative factor returns—specifically...

mathematics, the fundamental theorem of arithmetic, also called the unique factorization theorem and prime factorization theorem, states that every integer...

Bézout's theorem is a statement concerning the number of common zeros of n polynomials in n indeterminates. In its original form the theorem states that...

f(r)=0} , a property known as the factor theorem. Let f ( x ) = x 3 − 12 x 2 − 42 {\displaystyle f(x)=x^{3}-12x^{2}-42} . Polynomial division of f ( x...

Well-ordering theorem (mathematical logic) Wilkie's theorem (model theory) Zorn's lemma (set theory) 2-factor theorem (graph theory) Abel's binomial theorem (combinatorics)...

fundamental theorem of algebra, which asserts that every polynomial may be factored into linear factors, one for each root. The theorem, which is named...

2 + b 2 = c 2 . {\displaystyle a^{2}+b^{2}=c^{2}.} The theorem is named for the Greek philosopher Pythagoras, born around 570 BC. The theorem has been...

handshaking lemma) the number of vertices is always even. 2-factor theorem – related theorem by Petersen Petersen (1891). See for example Bouchet & Fouquet...

derivative by a variant of Euclid's algorithm for polynomials. Sturm's theorem expresses the number of distinct real roots of p located in an interval...

than 2. The cases n = 1 and n = 2 have been known since antiquity to have infinitely many solutions. The proposition was first stated as a theorem by Pierre...

in particular, the theorem that any bridgeless 3-regular graph can be decomposed into a l-factor and a 2-factor (Petersen's theorem). Between 1887 and...

1 2 + 2 2 , 13 = 2 2 + 3 2 , 17 = 1 2 + 4 2 , 29 = 2 2 + 5 2 , 37 = 1 2 + 6 2 , 41 = 4 2 + 5 2 . {\displaystyle 5=1^{2}+2^{2},\quad 13=2^{2}+3^{2},\quad...

two divisors share a common factor other than 1). The theorem is sometimes called Sunzi's theorem. Both names of the theorem refer to its earliest known...

relationship between factor prices and factor supplies. The equilibrium links Heckscher-Ohlin theorem with factor price equalization theorem. The critical assumption...

following theorems were first proposed and proven by Ludwig Sylow in 1872, and published in Mathematische Annalen. Theorem (1)—For every prime factor p with...

composition factors, up to permutation and isomorphism. This theorem can be proved using the Schreier refinement theorem. The Jordan–Hölder theorem is also...

if there is a bijection between their factor groups that sends each factor group to an isomorphic one. The theorem is named after the Austrian mathematician...

with proving mathematical theorems by computer programs. Automated reasoning over mathematical proof was a major motivating factor for the development of...

Bayes' theorem (alternatively Bayes' law or Bayes' rule, after Thomas Bayes) gives a mathematical rule for inverting conditional probabilities, allowing...

In probability theory, the central limit theorem (CLT) states that, under appropriate conditions, the distribution of a normalized version of the sample...

derived from representations of its two factors, using the Brahmagupta–Fibonacci identity. Two-square theorem—Denote the number of divisors of n {\displaystyle...

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...

In number theory, Euler's theorem (also known as the Fermat–Euler theorem or Euler's totient theorem) states that, if n and a are coprime positive integers...

In physics, the no-cloning theorem states that it is impossible to create an independent and identical copy of an arbitrary unknown quantum state, a statement...

Euclid's theorem is a fundamental statement in number theory that asserts that there are infinitely many prime numbers. It was first proven by Euclid...

Applying the binomial theorem to the last factor, = ∑ k 1 + k 2 + ⋯ + k m − 1 + K = n ( n k 1 , k 2 , … , k m − 1 , K ) x 1 k 1 x 2 k 2 ⋯ x m − 1 k m − 1...

two prime factors. In 2025, Daniel R. Johnston, Matteo Bordignon, and Valeriia Starichkova provided an explicit version of Chen's theorem: Every even...