8

Part of 2007 Switzerland - Final Round

Problems(1)

subset of 1-2007, one divides another

Source: Switzerland - 2007 Swiss MO Final Round p8

M\subset \{1, 2, 3, . . . , 2007\}

a set with the following property: Among every three numbers one can always choose two from

M

such that one is divisible by the other. How many numbers can

M

contain at most?

combinatoricsnumber theorydivisible