MathDB

Sum of powers

Source: APMC 2001

April 17, 2006

modular arithmeticnumber theory proposednumber theory

Problem Statement

Determine the number of positive integers

a

, so that there exist nonnegative integers

x_0,x_1,\ldots,x_{2001}

which satisfy the equation

\displaystyle a^{x_0} = \sum_{i=1}^{2001} a^{x_i}