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1 5 9 6 7 7 7 m o d 1 7 = 1 2 because 1 5 9 end up with the number 9 , and the last digit when we power 9 is always 1 , 9 , but the 2 exponents are all odd, so 9 is the last digit.
And 9 m o d 1 7 = ? ? , 1 9 m o d 1 7 = 2 , 2 9 m o d 1 7 = 1 2 , 3 9 m o d 1 7 = 5 , 4 9 m o d 1 7 = 1 5 , 5 9 m o d 1 7 = 8 , 6 9 m o d 1 7 = 1 , e t c . . So the answer is 1 2 .