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The smallest positive composite number and the first even perfect square. Four is the smallest even number appearing in a Pythagorean triple: 3, 4, 5. In the numerology of ...

Barnette's conjecture asserts that every 3-connected bipartite cubic planar graph is Hamiltonian. The only graph on nine or fewer vertices satisfying Barnette's conditions is ...

There are two definitions of the Carmichael function. One is the reduced totient function (also called the least universal exponent function), defined as the smallest integer ...

A colossally abundant number is a positive integer n for which there is a positive exponent epsilon such that (sigma(n))/(n^(1+epsilon))>=(sigma(k))/(k^(1+epsilon)) for all ...

If a is an arbitrary integer relatively prime to n and g is a primitive root of n, then there exists among the numbers 0, 1, 2, ..., phi(n)-1, where phi(n) is the totient ...

In order to find integers x and y such that x^2=y^2 (mod n) (1) (a modified form of Fermat's factorization method), in which case there is a 50% chance that GCD(n,x-y) is a ...

There are two sorts of transforms known as the fractional Fourier transform. The linear fractional Fourier transform is a discrete Fourier transform in which the exponent is ...

There are (at least) two graphs associated with Horton, illustrated above. The first is a graph on 96 nodes providing a counterexample to the Tutte conjecture that every ...

The diagonal slash "/" used as the bar between numerator and denominator of an in-line fraction (Bringhurst 1997, p. 284). The solidus is also called a diagonal. Special care ...

Roman (1984, p. 2) describes umbral calculus as the study of the class of Sheffer sequences. Umbral calculus provides a formalism for the systematic derivation and ...