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...

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

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

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)...

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...

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

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...

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...

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

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...

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...

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

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...

with complex coefficients can be factored into 1st-degree factors (that is one way of stating the fundamental theorem of algebra), it follows that every...

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...

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...

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

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...

In mechanics, the virial theorem provides a general equation that relates the average over time of the total kinetic energy of a stable system of discrete...

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...

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

In game theory, folk theorems are a class of theorems describing an abundance of Nash equilibrium payoff profiles in repeated games (Friedman 1971). The...

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...

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

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...