Evaluate the expression 5^160 (mod 13).?

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Note that 5^2 = 25 = -1 (mod 13).
==> 5^4 = (5^2)^2 = (-1)^2 = 1 (mod 13).

So, 5^160 = 5^(4 * 40) = (5^4)^40 = 1^40 = 1 (mod 13).

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