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...

naming everything after Euler, some discoveries and theorems are attributed to the first person to have proved them after Euler. Euler's sum of powers conjecture...

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...

lower-case letter chi). The Euler characteristic was originally defined for polyhedra and used to prove various theorems about them, including the classification...

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...

Byrkit (1970, p. 80) See Euler's theorem. L. Euler "Theoremata arithmetica nova methodo demonstrata" (An arithmetic theorem proved by a new method), Novi...

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...

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...

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...

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...

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...

Euler's formula, named after Leonhard Euler, is a mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric...

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

hemisphere cut out from a sphere of radius R. Its Euler characteristic is 1. On the left hand side of the theorem, we have K = 1 / R 2 {\displaystyle K=1/R^{2}}...

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...

Chern theorem (or the Chern–Gauss–Bonnet theorem after Shiing-Shen Chern, Carl Friedrich Gauss, and Pierre Ossian Bonnet) states that the Euler–Poincaré...

characteristic 0. The theorem was proven for two dimensions by Henri Poincaré and later generalized to higher dimensions by Heinz Hopf. The Euler characteristic...

known as the Euler product formula for the Riemann zeta function. Euler proved Newton's identities, Fermat's little theorem, Fermat's theorem on sums of...

geometry, the Gram–Euler theorem, Gram-Sommerville, Brianchon-Gram or Gram relation (named after Jørgen Pedersen Gram, Leonhard Euler, Duncan Sommerville...

millennia later, Leonhard Euler proved that all even perfect numbers are of this form. This is known as the Euclid–Euler theorem. It is not known whether...

Leonhard Euler (/ˈɔɪlər/ OY-lər; Swiss Standard German: [ˈleːɔnhard ˈɔʏlər]; German: [ˈleːɔnhaʁt ˈɔʏlɐ] ; 15 April 1707 – 18 September 1783) was a Swiss...

second factor zero, or they would not satisfy Fermat's little theorem. This is Euler's criterion. This proof only uses the fact that any congruence k...

still work out to ap − a, as needed.) This proof, due to Euler, uses induction to prove the theorem for all integers a ≥ 0. The base step, that 0p ≡ 0 (mod p)...

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...

In mathematics, the Euler–Maclaurin formula is a formula for the difference between an integral and a closely related sum. It can be used to approximate...

This proves Euclid's Theorem. In the same paper (Theorem 19) Euler in fact used the above equality to prove a much stronger theorem that was unknown before...

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

theorem was incorrect. In 1770, Leonhard Euler gave a proof of p = 3, but his proof by infinite descent contained a major gap. However, since Euler himself...

dynamics, the Euler equations are a set of partial differential equations governing adiabatic and inviscid flow. They are named after Leonhard Euler. In particular...