MathDB

China Mathematics Olympiads (National Round) 2008 Problem 4

Source:

November 28, 2010

number theory unsolvednumber theory

Problem Statement

Let

A

be an infinite subset of

\mathbb{N}

, and

n

a fixed integer. For any prime

p

not dividing

n

, There are infinitely many elements of

A

not divisible by

p

. Show that for any integer

m >1, (m,n) =1

, There exist finitely many elements of

A

, such that their sum is congruent to 1 modulo

m

and congruent to 0 modulo

n