We have: mn = p , n = mp, m = np

mp . np = p <=> mnp² = p

With p = 0, we have : m = n = p = 0

With p others 0, we have : mp . np = p <=> mnp = 1 <=> p² = 1

With p = 1, we have : mn = 1, m = n =>\(\left\{{}\begin{matrix}m=n=1\\m=n=-1\end{matrix}\right.\)

With P = -1, we have : mn = -1 , m= -n =>\(\left\{{}\begin{matrix}m=1,n=-1\\m=-1,n=1\end{matrix}\right.\)

So we have the sets of numbers (m, n ,p) satisfy is : (0;0;0), (1;1;1), (-1;-1;1), (1;-1;-1), (-1;1;-1)