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2014 MMATHS Tiebreaker p4 - min max n\sqrt5 - [ n\sqrt5]

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October 8, 2023
algebrainequalitiesMMATHS

Problem Statement

Determine, with proof, the maximum and minimum among the numbers 5−⌊5⌋,25−⌊25⌋,35−⌊35⌋,...,20135−⌊20135⌋,20145−⌊20145⌋\sqrt5 - \lfloor \sqrt5 \rfloor, 2\sqrt5 - \lfloor 2\sqrt5 \rfloor, 3\sqrt5 - \lfloor 3 \sqrt5\rfloor, ..., 2013\sqrt5 - \lfloor 2013\sqrt5\rfloor, 2014\sqrt5 - \lfloor 2014\sqrt5\rfloor
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