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Determining the maximum number of pieces in which it is possible to divide a circle for a given number of cuts is called the circle cutting or pancake cutting problem. The ...

Serre's problem, also called Serre's conjecture, asserts that the implication "free module ==> projective module" can be reversed for every module over the polynomial ring ...

The maximum number of pieces into which a cylinder can be divided by n oblique cuts is given by f(n) = (n+1; 3)+n+1 (1) = 1/6(n+1)(n^2-n+6) (2) = 1/6(n^3+5n+6), (3) where (a; ...

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 ...

The method for solving the Goursat problem and Cauchy problem for linear hyperbolic partial differential equations using a Riemann function.

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 ...

Brocard's conjecture states that pi(p_(n+1)^2)-pi(p_n^2)>=4 for n>=2, where pi(n) is the prime counting function and p_n is the nth prime. For n=1, 2, ..., the first few ...

The conjecture proposed by Catalan in 1888 and extended by E. Dickson that each aliquot sequence ends in a prime, a perfect number, or a set of sociable numbers. The ...

The generalized Riemann hypothesis conjectures that neither the Riemann zeta function nor any Dirichlet L-series has a zero with real part larger than 1/2. Compare with ...

Define the zeta function of a variety over a number field by taking the product over all prime ideals of the zeta functions of this variety reduced modulo the primes. Hasse ...