Let p be the remainder when 7^{84} is divided by 342 and q be the remainder when 7^{84} is divided by 344. What is (p-q) equal to?

Explanation

Note that 343 = 7^3. So 7^{84} = (7^3)^{28} = 343^{28}. Modulo 342, 343 \equiv 1, so p = 1^{28} = 1. Modulo 344, 343 \equiv -1, so q = (-1)^{28} = 1. Thus, p - q = 1 - 1 = 0.

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