# The unit digit a 5

Discrete Mathematics Level pending

Suppose $$m$$ and $$n$$ are two integers, not necessarily distinct, from the set $$\{1,2,3,...,800\}$$.

What is the probability that the unit digit of $$2^m+7^n$$ is $$5$$ ?

If the probability can be expressed as $$\dfrac{A}{B}$$ for co-prime positive integers $$A$$ and $$B$$, submit the value of $$A+B$$ as your answer.

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