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Let P, Q be integers satisfying D=P^2-4Q>0. (1) Then roots of x^2-Px+Q=0 (2) are a = 1/2(P+sqrt(D)) (3) b = 1/2(P-sqrt(D)), (4) so a+b = P (5) ab = 1/4(P^2-D) (6) = Q (7) a-b ...

The Paris-Harrington theorem is a strengthening of the finite Ramsey's theorem by requiring that the homogeneous set be large enough so that cardH>=minH. Clearly, the ...

A moment mu_n of a probability function P(x) taken about 0, mu_n^' = <x^n> (1) = intx^nP(x)dx. (2) The raw moments mu_n^' (sometimes also called "crude moments") can be ...

Self-recursion is a recursion that is defined in terms of itself, resulting in an ill-defined infinite regress. The formula for the volume of a cylinder leads to the ...

Given a number n, Fermat's factorization methods look for integers x and y such that n=x^2-y^2. Then n=(x-y)(x+y) (1) and n is factored. A modified form of this observation ...

Let G be a finite graph and v a vertex of G. The stabilizer of v, stab(v), is the set of group elements {g in Aut(G)|g(v)=v}, where Aut(g) is the graph automorphism group. ...

An Egyptian fraction is a sum of positive (usually) distinct unit fractions. The famous Rhind papyrus, dated to around 1650 BC contains a table of representations of 2/n as ...

The distance d(u,v) between two vertices u and v of a finite graph is the minimum length of the paths connecting them (i.e., the length of a graph geodesic). If no such path ...

Let a_1=1 and define a_(n+1) to be the least integer greater than a_n which cannot be written as the sum of at most h>=2 addends among the terms a_1, a_2, ..., a_n. This ...

A matching, also called an independent edge set, on a graph G is a set of edges of G such that no two sets share a vertex in common. It is not possible for a matching on a ...