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2017 preRMO p14, {x}, [x] , x in a geometric progression, min x^n > 100

Source:

August 9, 2019
algebrageometric progressionfloor functionInteger Partgeometric sequence

Problem Statement

Suppose xx is a positive real number such that {x},[x]\{x\}, [x] and xx are in a geometric progression. Find the least positive integer nn such that xn>100x^n > 100. (Here [x][x] denotes the integer part of xx and {x}=xāˆ’[x]\{x\} = x - [x].)
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