BD-BDMO 2016 Problem 1

(a) Show that $n(n + 1)(n + 2)$ is divisible by $6$ .

(b) Show that $1^{2015} + 2^{2015} + 3^{2015} + 4^{2015} + 5^{2015} + 6^{2015}$ is divisible by $7$ .