MathDB

Some cards each have a pair of numbers written on them. There is just one card for each pair

(a,b)

with

1 \leq a < b \leq 2003

. Two players play the following game. Each removes a card in turn and writes the product

ab

of its numbers on the blackboard. The first player who causes the greatest common divisor of the numbers on the blackboard to fall to

1

loses. Which player has a winning strategy?

Problem Statement