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Fermat's 4n+1 theorem, sometimes called Fermat's two-square theorem or simply "Fermat's theorem," states that a prime number p can be represented in an essentially unique ...

The continued fraction of A is [1; 3, 1, 1, 5, 1, 1, 1, 3, 12, 4, 1, 271, 1, ...] (OEIS A087501). A plot of the first 256 terms of the continued fraction represented as a ...

The center of a graph G is the set of vertices of graph eccentricity equal to the graph radius (i.e., the set of central points). In the above illustration, center nodes are ...

Arrange copies of the n digits 1, ..., n such that there is one digit between the 1s, two digits between the 2s, etc. For example, the unique (modulo reversal) n=3 solution ...

The first Göllnitz-Gordon identity states that the number of partitions of n in which the minimal difference between parts is at least 2, and at least 4 between even parts, ...

The Lucas-Lehmer test is an efficient deterministic primality test for determining if a Mersenne number M_n is prime. Since it is known that Mersenne numbers can only be ...

The Parts graphs are a set of unit-distance graphs with chromatic number five derived by Jaan Parts in 2019-2020 (Parts 2020a). They provide some of the smallest known ...

The first singular value k_1 of the elliptic integral of the first kind K(k), corresponding to K^'(k_1)=K(k_1), (1) is given by k_1 = 1/(sqrt(2)) (2) k_1^' = 1/(sqrt(2)). (3) ...

The n×n square matrix F_n with entries given by F_(jk)=e^(2piijk/n)=omega^(jk) (1) for j,k=0, 1, 2, ..., n-1, where i is the imaginary number i=sqrt(-1), and normalized by ...

Three types of n×n matrices can be obtained by writing Pascal's triangle as a lower triangular matrix and truncating appropriately: a symmetric matrix S_n with (S)_(ij)=(i+j; ...