MathDB
Question 2

Source: Iran TST 2006

April 29, 2006
ceiling functionlogarithmsalgebra proposedalgebra

Problem Statement

Let nn be a fixed natural number. a) Find all solutions to the following equation : ∑k=1n[x2k]=x−1 \sum_{k=1}^n [\frac x{2^k}]=x-1 b) Find the number of solutions to the following equation (mm is a fixed natural) : ∑k=1n[x2k]=x−m \sum_{k=1}^n [\frac x{2^k}]=x-m
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