MathDB

Counting subsets

Source: Romanian TST 4 2008, Problem 2

June 13, 2008

modular arithmeticnumber theory proposednumber theory

Problem Statement

Let

m, n \geq 1

be two coprime integers and let also

s

an arbitrary integer. Determine the number of subsets

A

of \{1, 2, ..., m \plus{} n \minus{} 1\} such that |A| \equal{} m and

\sum_{x \in A} x \equiv s \pmod{n}