sentences:  No two cold numbers can differ by a square, because if they did then a move from the larger of the two to the smaller would be winning, contradicting the assumption that they are both cold.Therefore, by the Furstenberg–Sárközy theorem, the natural density of the cold numbers is zero.That is, for every formula_5, and for all sufficiently large formula_1, the fraction of the numbers up to formula_1 that are cold is less than formula_8.