13

Part of 2013 India PRMO

Problems(1)

2013 preRMO p13, a,b \in {1,2,... ,1000}, 15/(a+b)

Source:

To each element of the set

S = \{1,2,... ,1000\}

a colour is assigned. Suppose that for any two elements

a, b

S

15

a + b

then they are both assigned the same colour. What is the maximum possible number of distinct colours used?

number theorymaximumdivides