MathDB

Mary and Pat play the following number game. Mary picks an initial integer greater than

2017

. She then multiplies this number by

2017

and adds

2

to the result. Pat will add

2019

to this new number and it will again be Mary’s turn. Both players will continue to take alternating turns. Mary will always multiply the current number by

2017

and add

2

to the result when it is her turn. Pat will always add

2019

to the current number when it is his turn. Pat wins if any of the numbers obtained by either player is divisible by

2018

. Mary wants to prevent Pat from winning the game. Determine, with proof, the smallest initial integer Mary could choose in order to achieve this.

Problem Statement