# Homework Help: Last digit, mod 8

1. Aug 14, 2010

### EV33

1. The problem statement, all variables and given/known data
What is the last digit of 101000 (mod 8)

2. Relevant equations

3. The attempt at a solution

10^2$$\equiv$$4 (mod 8)

(10^2)^500$$\equiv$$ 4^500 (mod 8)

4^2=0 (mod 8)

(4^2)^250$$\equiv$$0^250$$\equiv$$0 (mod 8)

Thus, the last digit is 0.

Are these steps mathematically legal?

Last edited: Aug 14, 2010
2. Aug 15, 2010

### praharmitra

ya, what you have done is absolutely fine

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