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The Cauchy product of two sequences f(n) and g(n) defined for nonnegative integers n is defined by (f degreesg)(n)=sum_(k=0)^nf(k)g(n-k).

A solitaire game played with cards. The chance of winning is 1/13, and the arithmetic mean of the number of cards turned up is 42.4.

A number puzzle in which a group of arithmetical operations has some or all of its digits replaced by letters or symbols, and where the original digits must be found. In such ...

A surface which is related to Cayley numbers.

Elementary methods consist of arithmetic, geometry, and high school algebra. These are the only tools that may be used in the branch of number theory known as elementary ...

Elementary number theory is the branch of number theory in which elementary methods (i.e., arithmetic, geometry, and high school algebra) are used to solve equations with ...

If a function phi is harmonic in a sphere, then the value of phi at the center of the sphere is the arithmetic mean of its value on the surface.

A geometric sequence is a sequence {a_k}, k=0, 1, ..., such that each term is given by a multiple r of the previous one. Another equivalent definition is that a sequence is ...

The identity PVint_(-infty)^inftyF(phi(x))dx=PVint_(-infty)^inftyF(x)dx (1) holds for any integrable function F(x) and phi(x) of the form ...

(theta_3(z,t)theta_4(z,t))/(theta_4(2z,2t))=(theta_3(0,t)theta_4(0,t))/(theta_4(0,2t))=(theta_2(z,t)theta_1(z,t))/(theta_1(2z,2t)), where theta_i are Jacobi theta functions. ...