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Real p≥1; ∃a,b,c,d∈S such that ab=cd

Source: Czech-Polish-Slovak Match 2007-P4

September 14, 2011
number theory unsolvednumber theory

Problem Statement

For any real number p≥1p\geq1 consider the set of all real numbers xx with p<x<(2+p+14)2.p<x<\left(2+\sqrt{p+\frac{1}{4}}\right)^2. Prove that from any such set one can select four mutually distinct natural numbers a,b,c,da, b, c, d with ab=cd.ab=cd.
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