MathDB

Two players alternately write integers on a blackboard as follows: the first player writes

a_1

arbitrarily, then the second player writes

a_2

arbitrarily, and thereafter a player writes a number that is equal to the sum of the two preceding numbers. The player after whose move the obtained sequence contains terms such that

a_i-a_j

and

a_{i+1}-a_{j+1}~(i\ne j)

are divisible by

1999

, wins the game. Which of the players has a winning strategy?

Problem Statement