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Find all positive reals r such that a set S exists

Source: 14th March 2013

April 1, 2013

inductionmodular arithmeticalgebra proposedalgebra

Problem Statement

Find all positive real numbers

r<1

such that there exists a set

\mathcal{S}

with the given properties: i) For any real number

t

, exactly one of

t, t+r

and

t+1

belongs to

\mathcal{S}

; ii) For any real number

t

, exactly one of

t, t-r

and

t-1

belongs to

\mathcal{S}