2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/60161If L, respectively R are matrices with entries binom{i-1,j-1}, respectively binom{i-1,n-j}, it is known that L^2 = I (mod 2), respectively R^3 = I (mod 2), where I is the identity matrix of dimension n > 1 (see P10735-May 1999 issue of the American Mathematical Monthly). We generalize it for any prime p, and give a beautiful connection to Fibonacci numbers.13 pagesCombinatoricsNumber Theory05A10; 11B39; 11B65; 11C20; 15A33text