Number Theory

[1^2009 + 2^2009 + 3^2009 + ... + 100^2009] mod 10^10 ==7532998500 - these are the last 10 digits.

What is the ones digit of 1^2009 + 2^2009 + 3^2009 + ... + 100^2009?  

0 (zero) ... Once you get a zero into the units position – and 10²⁰⁰⁹ is the first place it will be introduced – that zero stays there no matter how many times, or by what, you multiply it.  

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