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rectangle with dimensions a,b such no lattice point interior or on it's edge

Source: Germany Federal - Bundeswettbewerb Mathematik 2012, round 2, p4

April 15, 2020

rectanglecombinatoricscombinatorial geometrylattice pointslattice

Problem Statement

A rectangle with the side lengths

a

and

b

with

a <b

should be placed in a right-angled coordinate system so that there is no point with integer coordinates in its interior or on its edge. Under what necessary and at the same time sufficient conditions for

a

and

b

is this possible?

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