Question
Find the remainder when 5123 is divided by
36.Solution
φ(36) = φ(4×9) = φ(4)φ(9) = 2×6 = 12 Since gcd(5,36)=1, Euler’s theorem: 512 ≡ 1 (mod 36) Now 123 = 12×10 + 3 5123 ≡ (512)10 × 53 ≡ 110 × 125 ≡ 125 (mod 36) 125 ÷ 36 = 3×36 = 108, remainder 17 Answer: remainder = 17.
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