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Given a sum and a set of weights, find the weights which were used to generate the sum. The values of the weights are then encrypted in the sum. This system relies on the ...

Given a set S of n nonnegative integers, the number partitioning problem requires the division of S into two subsets such that the sums of number in each subset are as close ...

Kloosterman's sum is defined by S(u,v,n)=sum_(h)exp[(2pii(uh+vh^_))/n], (1) where h runs through a complete set of residues relatively prime to n and h^_ is defined by hh^_=1 ...

An exponential sum of the form sum_(n=1)^Ne^(2piiP(n)), (1) where P(n) is a real polynomial (Weyl 1914, 1916; Montgomery 2001). Writing e(theta)=e^(2piitheta), (2) a notation ...

The sum rule for differentiation states d/(dx)[f(x)+g(x)]=f^'(x)+g^'(x), (1) where d/dx denotes a derivative and f^'(x) and g^'(x) are the derivatives of f(x) and g(x), ...

Given a sequence {a_k}_(k=1)^n, a partial sum of the first N terms is given by S_N=sum_(k=1)^Na_k.

Let X be an arbitrary topological space. Denote the set closure of a subset A of X by A^- and the complement of A by A^'. Then at most 14 different sets can be derived from A ...

The sum of sets A and B in a vector space, equal to {a+b:a in A,b in B}.

A sum in which subsequent terms cancel each other, leaving only initial and final terms. For example, S = sum_(i=1)^(n-1)(a_i-a_(i+1)) (1) = ...

The problem of determining (or counting) the set of all solutions to a given problem.