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Fermat's 4n+1 theorem, sometimes called Fermat's two-square theorem or simply "Fermat's theorem," states that a prime number p can be represented in an essentially unique ...

The W polynomials obtained by setting p(x)=x and q(x)=1 in the Lucas polynomial sequence. (The corresponding w polynomials are called Lucas polynomials.) They have explicit ...

A free idempotent monoid is a monoid that satisfies the identity x^2=x and is generated by a set of elements. If the generating set of such a monoid is finite, then so is the ...

A board covered by a lattice of pegs around which one can span rubber bands to form segments and polygons. It was invented by the Egyptian mathematician and pedagogist Caleb ...

A googol is a large number equal to 10^(10^2)=10^(100) (i.e., a 1 with 100 zeros following it). Written out explicitly, ...

The join G=G_1+G_2 of graphs G_1 and G_2 with disjoint point sets V_1 and V_2 and edge sets X_1 and X_2 is the graph union G_1 union G_2 together with all the edges joining ...

For any prime number p and any positive integer n, the p^n-rank r_(p^n)(G) of a finitely generated Abelian group G is the number of copies of the cyclic group Z_(p^n) ...

The first Hardy-Littlewood conjecture is called the k-tuple conjecture. It states that the asymptotic number of prime constellations can be computed explicitly. A particular ...

A square matrix is called Hermitian if it is self-adjoint. Therefore, a Hermitian matrix A=(a_(ij)) is defined as one for which A=A^(H), (1) where A^(H) denotes the conjugate ...

There are a number of formulas variously known as Hurwitz's formula. The first is zeta(1-s,a)=(Gamma(s))/((2pi)^s)[e^(-piis/2)F(a,s)+e^(piis/2)F(-a,s)], where zeta(z,a) is a ...