1. ## Geometric progression

Find all real x>o such that x-[x], [x], x (where [x] denotes the greatest integer not greater than x) form a geometric progression.

2. Originally Posted by alexmahone
Find all real x>o such that x-[x], [x], x (where [x] denotes the greatest integer not greater than x) form a geometric progression.
write x=a+b, where a=[x] and 0<=b<1. Then the condition that b,a,a+b are a geometric progressions is:

a/b=(a+b)/a

solve this for a in terms of b then conclude what you must from the requirerment that a is an integer, then reconstruct x in terms of b.

CB