  If 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.
