MathDB
Digits of 2^n and 5^n

Source: Spring 2006 Tournament of Towns Junior A-Level #4

April 15, 2015
number theory

Problem Statement

Is there exist some positive integer nn, such that the first decimal of 2n2^n (from left to the right) is 55 while the first decimal of 5n5^n is 22?
(5 points)