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A Diophantine problem (i.e., one whose solution must be given in terms of integers) which seeks a solution to the following problem. Given n men and a pile of coconuts, each ...

Let rho(x)dx be the fraction of time a typical dynamical map orbit spends in the interval [x,x+dx], and let rho(x) be normalized such that int_0^inftyrho(x)dx=1 over the ...

A rational amicable pair consists of two integers a and b for which the divisor functions are equal and are of the form sigma(a)=sigma(b)=(P(a,b))/(Q(a,b))=R(a,b), (1) where ...

A minimum clique covering is a clique covering of minimum size, and the size of such a minimum clique covering is known as the clique covering number. Note that while a ...

The positions of the geometric centroid of a planar non-self-intersecting polygon with vertices (x_1,y_1), ..., (x_n,y_n) are x^_ = ...

A symplectic form on a smooth manifold M is a smooth closed 2-form omega on M which is nondegenerate such that at every point m, the alternating bilinear form omega_m on the ...

Let (K,|·|) be a non-Archimedean field. Its valuation ring R is defined to be R={x in K:|x|<=1}. The valuation ring has maximal ideal M={x in K:|x|<1}, and the field R/M is ...

An important result in valuation theory which gives information on finding roots of polynomials. Hensel's lemma is formally stated as follows. Let (K,|·|) be a complete ...

The tangent function is defined by tanx=(sinx)/(cosx), (1) where sinx is the sine function and cosx is the cosine function. The notation tgx is sometimes also used ...

An interval is a connected portion of the real line. If the endpoints a and b are finite and are included, the interval is called closed and is denoted [a,b]. If the ...