MathDB
First digit of Powers of an Integer

Source: Tournament of Towns Spring 2015 Senior A-level

February 24, 2017
number theory

Problem Statement

(a) The integers xx, x2x^2 and x3x^3 begin with the same digit. Does it imply that this digit is 11? (22 points)
(b) The same question for the integers x,x2,x3,,x2015x, x^2, x^3, \cdots, x^{2015} (33 points) .