Question
Find the remainder when 798 is divided by 5.
Solution
7 ≡ 2 (mod 5) So 798 ≡ 298 (mod 5) Powers of 2 mod 5: 2¹ ≡ 2 2² ≡ 4 2³ ≡ 8 ≡ 3 2⁴ ≡ 16 ≡ 1 Pattern length = 4 98 ÷ 4 gives remainder 2 So 298 ≡ 2² ≡ 4 (mod 5) Remainder = 4
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