Question 6
Prove that
a) $\displaystyle\sum_{k=1}^{1008}k\binom{2017}{k}\equiv0\pmod{2017^2}$;
b) $\displaystyle\sum_{k=1}^{504}(-1)^k\binom{2017}{k}\equiv3(2^{2016}-1)\pmod{2017^2}$.
a) $\displaystyle\sum_{k=1}^{1008}k\binom{2017}{k}\equiv0\pmod{2017^2}$;
b) $\displaystyle\sum_{k=1}^{504}(-1)^k\binom{2017}{k}\equiv3(2^{2016}-1)\pmod{2017^2}$.