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Let the values of a function f(x) be tabulated at points x_i equally spaced by h=x_(i+1)-x_i, so f_1=f(x_1), f_2=f(x_2), ..., f_n=f(x_n). Then Durand's rule approximating the ...

A graph G with m edges is said to be elegant if the vertices of G can be labeled with distinct integers (0,1,2,...,m) in such a way that the set of values on the edges ...

There exists an absolute constant C such that for any positive integer m, the discrepancy of any sequence {alpha_n} satisfies ...

A generalization of Fermat's little theorem. Euler published a proof of the following more general theorem in 1736. Let phi(n) denote the totient function. Then a^(phi(n))=1 ...

A system of congruences a_i mod n_i with 1<=i<=k is called a complete residue system (or covering system) if every integer y satisfies y=a_i (mod n) for at least one value of ...

A map psi:M->M, where M is a manifold, is a finite-to-one factor of a map Psi:X->X if there exists a continuous surjective map pi:X->M such that psi degreespi=pi degreesPsi ...

A functional graph is a directed graph in which each vertex has outdegree one, and can therefore be specified by a function mapping {1,...,n} onto itself. Functional graphs ...

A disk D in a solid torus V=S^1×D^2 is called meridinal if its boundary is a nontrivial curve in del V (so that it is a meridian). Then a closed subset X subset V is called ...

Let a Gram point g_n be called "good" if (-1)^nZ(g_n)>0, and "bad" otherwise (Rosser et al. 1969; Edwards 2001, p. 180). Then the interval between two consecutive good Gram ...

Let the values of a function f(x) be tabulated at points x_i equally spaced by h=x_(i+1)-x_i, so f_1=f(x_1), f_2=f(x_2), ..., f_7=f(x_7). Then Hardy's rule approximating the ...