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Homework Statement
What is the last digit of 101000 (mod 8)
Homework Equations
The Attempt at a Solution
10^2[tex]\equiv[/tex]4 (mod 8)
(10^2)^500[tex]\equiv[/tex] 4^500 (mod 8)
4^2=0 (mod 8)
(4^2)^250[tex]\equiv[/tex]0^250[tex]\equiv[/tex]0 (mod 8)
Thus, the last digit is 0.
Are these steps mathematically legal?
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