What is the remainder when (17^{25} + 19^{25}) is divided by 18?

Explanation

Using modular arithmetic, 17 \equiv -1 \pmod{18} and 19 \equiv 1 \pmod{18}. Therefore, 17^{25} + 19^{25} \equiv (-1)^{25} + (1)^{25} \equiv -1 + 1 \equiv 0 \pmod{18}. The remainder is 0.

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