# Alternating last digits

Algebra Level 3

Let $$A$$ be a single digit positive integer such that

• the last digit of $$A, A^3, A^5, A^7$$ are all the same, and it is equal to $$B$$.
• the last digit of $$A^2 ,A^4, A^6, A^8$$ are all the same, and it is equal to $$C$$.

If $$B$$ and $$C$$ are distinct digits. What is $$B+C$$?

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