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A composite number n is a positive integer n>1 which is not prime (i.e., which has factors other than 1 and itself). The first few composite numbers (sometimes called ...

If a discrete group of displacements in the plane has more than one center of rotation, then the only rotations that can occur are by 2, 3, 4, and 6. This can be shown as ...

C_4 is one of the two groups of group order 4. Like C_2×C_2, it is Abelian, but unlike C_2×C_2, it is a cyclic. Examples include the point groups C_4 (note that the same ...

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 ...