MathDB

Prove that a subset of N exist

Source:

August 28, 2010

inductionratioarithmetic sequencealgebra unsolvedalgebra

Problem Statement

Let

\mathbb N = B_1\cup\cdots \cup B_q

be a partition of the set

\mathbb N

of all positive integers and let an integer

l \in \mathbb N

be given. Prove that there exist a set

t \in T

of cardinality

Y \subset X

, an infinite set

T \subset \mathbb N

, and an integer

k

with

1 \leq k \leq q

such that for any

t \in T

and any finite set

Y \subset X

, the sum

t+ \sum_{y \in Y} y

belongs to

B_k.

Back to Problems View on AoPS