1

Part of 2024 Silk Road

Problems(1)

Source: Silk Road 2024 P1

n

be a positive integer and let

p, q>n

be odd primes. Prove that the positive integers

1, 2, \ldots, n

can be colored in

2

colors, such that for any

x \neq y

of the same color,

xy-1

is not divisible by

p

q