Euler's criterion

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Euler's criterion

[′ȯi·lərz krī′tir·ē·ən]

(mathematics)

A criterion for the congruence x ⁿ≡ a (mod m) to have a solution, namely that a ^φ/d≡1 (mod m), where φ = φ(m) is Euler's phi function evaluated at m, and d is the greatest common divisor of φ and n.

References in periodicals archive ?

For any integer a with (a, p) = 1, from the Euler's criterion (See Theorem 9.2 of [4]) we know that

Some identities involving Bernoulli numbers and Euler numbers

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Euler number (physics)
Euler number (topology)
Euler number 1
Euler number 2
Euler Number/Tissue Volume
Euler numbers
Euler path
Euler phi-function
Euler polyhedron theorem
Euler quadratic residue theorem
Euler rotation
Euler Substitutions
Euler summation formula
Euler theorem
Euler theorem on homogeneous functions
Euler totient rule
Euler totient theorem
Euler tour
Euler trail
Euler transformation
Euler Venn diagram
Euler walk
Euler wenn diagram
Euler zeta function
Euler's angle
Euler's Box
Euler's Box
Euler's Box
Euler's circles
Euler's constant
Euler's criterion
Euler's equation
Euler's equation of motion
Euler's equations
Euler's equations of motion
Euler's expansion
Euler's formula
Euler's formula for polyhedra
Euler's formula in complex analysis
Euler's forward method
Euler's generalization
Euler's homogeneous function theorem
Euler's Integral
Euler's method
Euler's numbers
Euler's phi function
Euler's polyhedron formula
Euler's polyhedron theorem
Euler's quadratic residue theorem
Euler's spiral
Euler's summation formula
Euler's theorem
Euler's theorem on homogeneous functions
Euler's totient function
Euler's totient function
Euler's totient rule
Euler's totient theorem
Euler, Leonhard
Euler, Leonhard
Euler, Leonhard
Euler, Ulf Svante von
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