Question
Find the remainder when 3⁶⁵ is divided by 8.
Solution
3¹ ≡ 3 (mod 8) 3² = 9 ≡ 1 (mod 8) Powers of 3 mod 8 repeat every 2: 3, 1, 3, 1, ... Since 65 is odd, 3⁶⁵ ≡ 3¹ ≡ 3 (mod 8) Remainder = 3
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