MathDB

Combo NT

Source: Silk Road 2024 P1

October 20, 2024

number theory

Problem Statement

Let

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

and

q

.

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