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The two recursive sequences U_n = mU_(n-1)+U_(n-2) (1) V_n = mV_(n-1)+V_(n-2) (2) with U_0=0, U_1=1 and V_0=2, V_1=m, can be solved for the individual U_n and V_n. They are ...

The term "biquadratic equation" is sometimes used to as a synonym for quartic equation (Beyer 1987b, p. 34), but perhaps more commonly (e.g., Hazewinkel 1988; Gellert et al. ...

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 ...

The central beta function is defined by beta(p)=B(p,p), (1) where B(p,q) is the beta function. It satisfies the identities beta(p) = 2^(1-2p)B(p,1/2) (2) = ...

The Chebotarev density theorem is a complicated theorem in algebraic number theory which yields an asymptotic formula for the density of prime ideals of a number field K that ...

The downward Clenshaw recurrence formula evaluates a sum of products of indexed coefficients by functions which obey a recurrence relation. If f(x)=sum_(k=0)^Nc_kF_k(x) (1) ...

Codimension is a term used in a number of algebraic and geometric contexts to indicate the difference between the dimension of certain objects and the dimension of a smaller ...

The Copeland-Erdős constant is the constant with decimal expansion 0.23571113171923... (OEIS A033308) obtained by concatenating consecutive primes: 2, 23, 235, 2357, 235711, ...

An order-n Costas array is a permutation on {1,...,n} such that the distances in each row of the triangular difference table are distinct. For example, the permutation ...

A special case of Apollonius' problem requiring the determination of a circle touching three mutually tangent circles (also called the kissing circles problem). There are two ...