Find the remainder: \( (17^{13} - 21) \div 18 \).
14
We need to find the remainder when \( 17^{13} - 21 \) is divided by 18.
Step 1: Apply Fermat’s Theorem:
\( 17 \equiv -1 \pmod{18} \).
Step 2: Compute \( 17^{13} \) mod 18:
\( (-1)^{13} \equiv -1 \pmod{18} \).
Step 3: Compute \( (-1 - 21) \mod 18 \):
\( -22 \mod 18 = 14 \).
Thus, the remainder is 14.
The correct answer is option 1.
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