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there are 2 numbers in A whose difference is a or b

Source: Mathematics Regional Olympiad of Mexico Center Zone 2010 P4

November 10, 2021

combinatorics

Problem Statement

Let

a

and

b

be two positive integers and

A

be a subset of

\{1, 2,…, a + b \}

that has more than

\frac {a + b} {2}

elements. Show that there are two numbers in

A

whose difference is

a

b