Some cards each have a pair of numbers written on them. There is just one card for each pair (a,b) with 1≤a<b≤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? number theorygreatest common divisorcombinatorics unsolvedcombinatorics