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A problem posed by the Slovak mathematician Stefan Znám in 1972 asking whether, for all integers k>=2, there exist k integers x_1,...,x_k all greater than 1 such that x_i is ...

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 ...

The complementary subspace problem asks, in general, which closed subspaces of a Banach space are complemented (Johnson and Lindenstrauss 2001). Phillips (1940) proved that ...

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.

A "weird number" is a number that is abundant (i.e., the sum of proper divisors is greater than the number) without being pseudoperfect (i.e., no subset of the proper ...

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 ...

A Mrs. Perkins's quilt is a dissection of a square of side n into a number of smaller squares. The name "Mrs. Perkins's Quilt" comes from a problem in one of Dudeney's books, ...