system of inequalities, number of integer solutions
Source: Mongolia MO 2000 Grade 10 P5
April 22, 2021
inequalitiescombinatorics
Problem Statement
Given a natural number , find the number of quadruples of integers with satisfy the following inequalities:
\begin{align*}
&1\le v+x-y\le n,\\
&1\le x+y-u\le n,\\
&1\le u+v-y\le n,\\
&1\le v+x-u\le n.
\end{align*}