Pascalʹs Triangle (mod 8)

Lucasʹ theorem gives a congruence for a binomial coefficient modulo a prime. Davis and Webb (Europ. J. Combinatorics,11(1990), 229–233) extended Lucasʹ theorem to a prime power modulus. Making use of their result, we count the number of times each residue class occurs in thenth row of Pascalʹs triangle (mod 8). Our results correct and extend those of Granville (Amer. Math. Monthly,99(1992), 318–331).