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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