MathDB
How Many Integer Solutions?

Source: Spring 2006 Tournament of Towns Senior O-Level #3

September 9, 2015
inequalities

Problem Statement

Let aa be some positive number. Find the number of integer solutions xx of inequality 100<xa<1000100 < xa < 1000 given that inequality 10<xa<10010 < xa < 100 has exactly 55 integer solutions. Consider all possible cases.
(4 points)
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