Y by Adventure10, MethMath, Mango247
Determine the number of positive integers
, so that there exist nonnegative integers
which satisfy the equation
![\[ \displaystyle a^{x_0} = \sum_{i=1}^{2001} a^{x_i} \]](//latex.artofproblemsolving.com/d/1/4/d1475cfe401dcb54c47c9c5345994e61f81c3d14.png)


![\[ \displaystyle a^{x_0} = \sum_{i=1}^{2001} a^{x_i} \]](http://latex.artofproblemsolving.com/d/1/4/d1475cfe401dcb54c47c9c5345994e61f81c3d14.png)
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