MathDB

14

Part of 2017 India PRMO

Problems(1)

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

Source:

8/9/2019
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].)
algebrageometric progressionfloor functionInteger Partgeometric sequence