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k-element subsets = (2n-k)*(2-element)

Source: Bulgarian TST 2007 for Balkan MO and ARO, II day Problem 2

April 9, 2007

inequalitiesnumber theory proposednumber theory

Problem Statement

Let

n,k

be positive integers such that

n\geq2k>3

and

A= \{1,2,...,n\}.

Find all

n

and

k

such that the number of

k

-element subsets of

A

2n-k

times bigger than the number of

2

-element subsets of

A.