In mathematics, the Euler numbers are a sequence En of integers (sequence A122045 in the OEIS) defined by the Taylor series expansion 1 cosh ⁡ t = 2 e...

Euler's "lucky" numbers are positive integers n such that for all integers k with 1 ≤ k < n, the polynomial k2 − k + n produces a prime number. When k...

mathematician Leonhard Euler (1707–1783), who made many important discoveries and innovations. Many of these items named after Euler include their own unique...

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

in the Euler–Maclaurin formula, and in expressions for certain values of the Riemann zeta function. The values of the first 20 Bernoulli numbers are given...

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...

The numbers An are variously known as Euler numbers, zigzag numbers, up/down numbers, or by some combinations of these names. The name Euler numbers in...

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

algebraic topology and polyhedral combinatorics, the Euler characteristic (or Euler number, or Euler–Poincaré characteristic) is a topological invariant...

this definition is the fact that all prime numbers n satisfy the above equation, as explained in the Euler's criterion article. The equation can be tested...

sometimes called Euler's number, after the Swiss mathematician Leonhard Euler, though this can invite confusion with Euler numbers, or with Euler's constant,...

n is 1 itself, and gcd(1, 1) = 1. Euler's totient function is a multiplicative function, meaning that if two numbers m and n are relatively prime, then...

exist absolute Euler pseudoprimes, numbers which are Euler pseudoprimes to every base relatively prime to themselves. The absolute Euler pseudoprimes are...

The 18th-century Swiss mathematician Leonhard Euler (1707–1783) is among the most prolific and successful mathematicians in the history of the field....

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...

rational numbers are all rescalings of integer solutions. Given an Euler brick with edge-lengths (a, b, c), the triple (bc, ac, ab) constitutes an Euler brick...

wrong. The errors can in fact be predicted; they are generated by the Euler numbers En according to the asymptotic formula π 2 − 2 ∑ k = 1 N / 2 ( − 1 )...

combine the Bernoulli numbers and binomial coefficients. They are used for series expansion of functions, and with the Euler–MacLaurin formula. These...

primes, in a 1742 letter to Euler. Euler proved Alhazen's conjecture (now the Euclid–Euler theorem) that all even perfect numbers can be constructed from...

The Riemann zeta function or Euler–Riemann zeta function, denoted by the Greek letter ζ (zeta), is a mathematical function of a complex variable defined...

full-scale Reynolds number, and similarly for the Euler numbers. The model numbers and design numbers should be in the same proportion, hence p m ρ m v...

prime numbers, then 2n × p × q and 2n × r are a pair of amicable numbers. Thābit ibn Qurra's theorem corresponds to the case m = n − 1. Euler's rule creates...

logarithm, also commonly written as ln(x) or loge(x). Euler's constant (sometimes called the Euler–Mascheroni constant) is a mathematical constant, usually...

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...

multiples of itself. Among irrational numbers are the ratio π of a circle's circumference to its diameter, Euler's number e, the golden ratio φ, and the...

P}{\frac {1}{p}}} is divergent, where P denotes the set of all prime numbers (Euler writes that the infinite sum equals log ⁡ log ⁡ ∞ {\displaystyle \log...

Two 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...

the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. Some start counting with 0, defining the natural numbers as the non-negative...

In number theory, an Euler product is an expansion of a Dirichlet series into an infinite product indexed by prime numbers. The original such product...

An Euler diagram (/ˈɔɪlər/, OY-lər) is a diagrammatic means of representing sets and their relationships. They are particularly useful for explaining...