It is shown that the integer linear programming problem with a fixed number of variables is polynomially solvable. The proof depends on methods from geometry of numbers.

A prime number is an integer, or whole number, that has only two factors — 1 and itself. Put another way, a prime number can be divided evenly only by 1 and by itself. Prime numbers also must be ...

Thomas A. Lambe, Upper Bound on the Number of Nonnegative Integer Solutions to a Linear Equation, SIAM Journal on Applied Mathematics, Vol. 32, No. 1 (Jan., 1977), pp. 215-219 ...

Blue Wizard: I have a positive integer number of children, whose ages are positive integers. The sum of their ages is the number of this bus, while the product is my own age.