Question 96
Kati and Peeter play the following game. First, Kati writes a positive integer $a \gt 2016$ on the blackboard. Then Peeter starts to write more numbers on the blackboard, adding at each step the number $2016b + 1$ where $b$ is the biggest number on the blackboard. Peeter wins if at some point he writes a number divisible by $2017$. Otherwise Kati wins. Can Kati win, and if yes, what is the smallest number $a$ she can write to win?