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IMO ShortList 1998, number theory problem 2

Source: IMO ShortList 1998, number theory problem 2

October 22, 2004
floor functionnumber theoryalgebraic identitiesalgebraIMO Shortlist

Problem Statement

Determine all pairs (a,b)(a,b) of real numbers such that a⌊bn⌋=b⌊an⌋a \lfloor bn \rfloor =b \lfloor an \rfloor for all positive integers nn. (Note that ⌊x⌋\lfloor x\rfloor denotes the greatest integer less than or equal to xx.)
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