# Alternating sum of sum of powers?

Level pending

If $$n$$ is a positive integer with a unit digit of $$5$$. Denote $$N$$ as the alternating sum of $$( 12^n + 9^n + 8^n + 6^n)$$. What is the sum of all possible values of $$M = N \bmod {11}$$ ?

Details and assumptions: As an explicit example, the alternating sum of $$43576 = 4 - 3 + 5 - 7 + 6 = 5$$

×