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A problem is an exercise whose solution is desired. Mathematical "problems" may therefore range from simple puzzles to examination and contest problems to propositions whose ...

A problem in the calculus of variations. Let a vessel traveling at constant speed c navigate on a body of water having surface velocity u = u(x,y) (1) v = v(x,y). (2) The ...

A bounded plane convex region symmetric about a lattice point and with area >4 must contain at least three lattice points in the interior. In n dimensions, the theorem can be ...

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

Given an expression involving known constants, integration in finite terms, computation of limits, etc., the constant problem is the determination of if the expression is ...

A problem is assigned to the NP (nondeterministic polynomial time) class if it is solvable in polynomial time by a nondeterministic Turing machine. A P-problem (whose ...

The question of whether a solution to a given problem exists. The existence problem can be solved in the affirmative without actually finding a solution to the original ...

A problem is NP-hard if an algorithm for solving it can be translated into one for solving any NP-problem (nondeterministic polynomial time) problem. NP-hard therefore means ...

A problem is assigned to the P (polynomial time) class if there exists at least one algorithm to solve that problem, such that the number of steps of the algorithm is bounded ...

A problem in the theory of algebraic invariants that was solved by Hilbert using an existence proof.