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Find two sets of successive integers

Source: 2017 Korea Winter Program Practice Test 2 #1

August 14, 2019

number theory

Problem Statement

For every positive integers

n,m

, show that there exist two sets

A,B

which satisfy the following.
[*]

A

is a set of

n

successive positive integers, and

B

is a set of

m

successive positive integers. [*]

A\cup B = \phi

[*]For every

a\in A

and

b\in B

a

and

b

are not relatively prime.