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 geometry, Euler's rotation theorem states that, in three-dimensional space, any displacement of a rigid body such that a point on the rigid body remains...

squares. Euler's identity may also refer to the pentagonal number theorem. Euler's number, e = 2.71828 . . . , the base of the natural logarithm Euler's idoneal...

In geometry, Euler's theorem states that the distance d between the circumcenter and incenter of a triangle is given by d 2 = R ( R − 2 r ) {\displaystyle...

little theorem are known. It is frequently proved as a corollary of Euler's theorem. Euler's theorem is a generalization of Fermat's little theorem: For...

Euler's quadrilateral theorem or Euler's law on quadrilaterals, named after Leonhard Euler (1707–1783), describes a relation between the sides of a convex...

also referred to as Euler's totient function, the Euler totient, or Euler's totient. Jordan's totient is a generalization of Euler's. The cototient of n...

which has Euler characteristic 2. This viewpoint is implicit in Cauchy's proof of Euler's formula given below. There are many proofs of Euler's formula...

Adleman used Fermat's little theorem to explain why RSA works, it is common to find proofs that rely instead on Euler's theorem. We want to show that med...

Euler's identity (also known as Euler's equation) is the equality e i π + 1 = 0 {\displaystyle e^{i\pi }+1=0} where e {\displaystyle e} is Euler's number...

generates one even perfect number, and vice versa. After Euler's proof of the Euclid–Euler theorem, other mathematicians have published different proofs...

Eruditorum, 1744 The title page of Euler's Methodus inveniendi lineas curvas Euler's 1760 world map Euler's 1753 map of Africa Euler is listed by an academic genealogy...

complex vector space can be considered as real vector spaces. Euler's homogeneous function theorem is a characterization of positively homogeneous differentiable...

valid if x is a complex number, and is also called Euler's formula in this more general case. Euler's formula is ubiquitous in mathematics, physics, chemistry...

the extended Euclidean algorithm, Euler's theorem may be used to compute modular inverses. According to Euler's theorem, if a is coprime to m, that is,...

posthumously in 1873 by Carl Hierholzer. This is known as Euler's Theorem: A connected graph has an Euler cycle if and only if every vertex has an even number...

In mathematics, the Goldbach–Euler theorem (also known as Goldbach's theorem), states that the sum of 1/(p − 1) over the set of perfect powers p, excluding...

rearrangement of the latter. This method can also be used to prove Euler's theorem, with a slight alteration in that the numbers from 1 to p − 1 are substituted...

mathematical field of differential geometry, Euler's theorem is a result on the curvature of curves on a surface. The theorem establishes the existence of principal...

useful from a numerical point of view). The Euler equations first appeared in published form in Euler's article "Principes généraux du mouvement des...

important theorems relating to modular arithmetic: Carmichael's theorem Chinese remainder theorem Euler's theorem Fermat's little theorem (a special...

and the Goldbach–Euler Theorem. He had a close friendship with famous mathematician Leonhard Euler, serving as inspiration for Euler's mathematical pursuits...

prime numbers are distributed. Euler's work in this area led to the development of the prime number theorem. Euler's great interest in number theory...

obtain at once Wilson's theorem, Euler's criterion, and (by squaring both sides of Euler's criterion) Fermat's little theorem. Example 1: Finding primes...

{\tfrac {B}{2}}\pm {\sqrt {-z}}\cos {\tfrac {C}{2}}}&=0\end{aligned}}} Euler's theorem states that in a triangle: ( R − r ) 2 = d 2 + r 2 , {\displaystyle...

the Euler characteristic of the 2-sphere is two. Therefore, there must be at least one zero. This is a consequence of the Poincaré–Hopf theorem. In the...

theory) Euclid–Euler theorem (number theory) Euler's theorem (number theory) Fermat's Last Theorem (number theory) Fermat's little theorem (number theory)...

Pick's theorem (proved in a different way) as the basis for a proof of Euler's formula. Alternative proofs of Pick's theorem that do not use Euler's formula...

Poincaré–Hopf theorem (also known as the Poincaré–Hopf index formula, Poincaré–Hopf index theorem, or Hopf index theorem) is an important theorem that is used...

restates the much stronger Theorem 19 (described below) in the paper of his former proof. Havil, Julian (2003). Gamma: Exploring Euler's Constant. Princeton...