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theory. Euler is regarded as one of the greatest, most prolific mathematicians in history and the greatest of the 18th century. Several great mathematicians...

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

combinatorics, the Euler characteristic (or Euler number, or Euler–Poincaré characteristic) is a topological invariant, a number that describes a topological...

In geometry, the Euler line, named after Leonhard Euler (/ˈɔɪlər/), is a line determined from any triangle that is not equilateral. It is a central line...

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 can be traced...

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...

has great historical importance in showing the practical feasibility of the RSA cryptosystem. The Solovay–Strassen test is essentially an Euler–Jacobi...

an Euler brick, named after Leonhard Euler, is a rectangular cuboid whose edges and face diagonals all have integer lengths. A primitive Euler brick...

that every even number is the sum of two primes, in a 1742 letter to Euler. Euler proved Alhazen's conjecture (now the Euclid–Euler theorem) that all...

pivotal role in analytic number theory and has applications in physics, probability theory, and applied statistics. Leonhard Euler first introduced and studied...

eventually to the definition of a new number: a square root of −1, denoted by i, a symbol assigned by Leonhard Euler, and called the imaginary unit. The...

Euler's factorization method is a technique for factoring a number by writing it as a sum of two squares in two different ways. For example the number...

modern number theory, after Fermat's relative lack of success in getting his contemporaries' attention for the subject. Euler's work on number theory...

the formula yielded only every even perfect number. It was not until the 18th century that Leonhard Euler proved that the formula 2 p − 1 ( 2 p − 1 )...

through his letters, kept Euler focused on number theory in the 1730s by discussing Fermat's conjecture with Euler. Euler subsequently offered a proof...

the Basel problem. Leonhard Euler solved it in 1735 when he showed it was equal to π2/6. Euler's result leads to the number theory result that the probability...

primes). The sum of Euler's totient function φ(x) over the first twenty-two integers is 150. 150 is a Harshad number and an abundant number. 150 degrees is...

Euler transform of -1, -2, ..., -34 1789 = number of wiggly sums adding to 17 (terms alternately increase and decrease or vice versa) 1790 = number of...

volunteered by Luke Durant to the Great Internet Mersenne Prime Search (GIMPS). A prime number is a natural number greater than 1 with no divisors other...

Multiplicative order Discrete logarithm Quadratic residue Euler's criterion Legendre symbol Gauss's lemma (number theory) Congruence of squares Luhn formula Mod...

antiquity because of their close connection to perfect numbers: the Euclid–Euler theorem asserts a one-to-one correspondence between even perfect numbers...