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The ratio of two numbers r and s is written r/s, where r is the numerator and s is the denominator. The ratio of r to s is equivalent to the quotient r/s. Betting odds ...

Any system of phi(n) integers, where phi(n) is the totient function, representing all the residue classes relatively prime to n is called a reduced residue system (Nagell ...

A removable singularity is a singular point z_0 of a function f(z) for which it is possible to assign a complex number in such a way that f(z) becomes analytic. A more ...

The root lattice of a semisimple Lie algebra is the discrete lattice generated by the Lie algebra roots in h^*, the dual vector space to the Cartan subalgebra.

A cross also called the tau cross or crux commissa, illustrated schematically above in polyomino form.

For any real number r>=0, an irrational number alpha can be approximated by infinitely many rational fractions p/q in such a way that ...

A 10-digit number satisfying the following property. Number the digits 0 to 9, and let digit n be the number of ns in the number. There is exactly one such number: 6210001000.

A Shanks (a,b)-chain is a sequence of primes p_i of the form p_(i+1)=ap_i^2-b, with a and b integers. On Sep. 1, 2000, P. Leyland found a (4, 17)-chain of length 6, and on ...

The transformation T(x) = frac(1/x) (1) = 1/x-|_1/x_|, (2) where frac(x) is the fractional part of x and |_x_| is the floor function, that takes a continued fraction ...

A set having exactly one element a. A singleton set is denoted by {a} and is the simplest example of a nonempty set.