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A problem is an exercise whose solution is desired. Mathematical "problems" may therefore range from simple puzzles to examination and contest problems to propositions whose ...

The angles mpi/n (with m,n integers) for which the trigonometric functions may be expressed in terms of finite root extraction of real numbers are limited to values of m ...

A prime number (or prime integer, often simply called a "prime" for short) is a positive integer p>1 that has no positive integer divisors other than 1 and p itself. More ...

The (lower) domination number gamma(G) of a graph G is the minimum size of a dominating set of vertices in G, i.e., the size of a minimum dominating set. This is equivalent ...

The number of representations of n by k squares, allowing zeros and distinguishing signs and order, is denoted r_k(n). The special case k=2 corresponding to two squares is ...

Count the number of lattice points N(r) inside the boundary of a circle of radius r with center at the origin. The exact solution is given by the sum N(r) = ...

An independent vertex set of a graph G is a subset of the vertices such that no two vertices in the subset represent an edge of G. The figure above shows independent sets ...

Number theory is a vast and fascinating field of mathematics, sometimes called "higher arithmetic," consisting of the study of the properties of whole numbers. Primes and ...

A right triangle is triangle with an angle of 90 degrees (pi/2 radians). The sides a, b, and c of such a triangle satisfy the Pythagorean theorem a^2+b^2=c^2, (1) where the ...

N_phi(m) is the number of integers n for which the totient function phi(n)=m, also called the multiplicity of m (Guy 1994). Erdős (1958) proved that if a multiplicity occurs ...