MathDB

6

Part of 1977 IMO Shortlist

Problems(1)

Integer solutions of the system of inequalities

Source:

9/20/2010
Let nn be a positive integer. How many integer solutions (i,j,k,l), 1≤i,j,k,l≤n(i, j, k, l) , \ 1 \leq i, j, k, l \leq n, does the following system of inequalities have:
1≤−j+k+l≤n1 \leq -j + k + l \leq n1≤i−k+l≤n1 \leq i - k + l \leq n1≤i−j+l≤n1 \leq i - j + l \leq n1≤i+j−k≤n ?1 \leq i + j - k \leq n \ ?
combinatoricsalgebracountinginequality systemIMO Shortlist