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Find the last digit of a sum

Source: Central American Olympiad 2006, Problem 1

April 30, 2007
modular arithmeticgeometry3D geometry

Problem Statement

For 0≤d≤90 \leq d \leq 9, we define the numbers Sd=1+d+d2+⋯+d2006S_{d}=1+d+d^{2}+\cdots+d^{2006}Find the last digit of the number S0+S1+⋯+S9.S_{0}+S_{1}+\cdots+S_{9}.
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