IMO 1977 SL 6

Let n be a positive integer. How many integer solutions

imoshortlistmathematicsolympiad

IMO 1977 SL 6

Origin: GDR

Problem

Let n be a positive integer. How many integer solutions (i, j, k, l), 1 \leqi, j, k, l \leqn, does the following system of inequalities have: 1 \leq−j + k + l \leqn 1 \leq i −k + l \leqn 1 \leq i −j + l \leqn 1 \leq i + j −k \leqn ?