Question
Find the remainder when 5123 is divided by 36.
Solution
Ο(36) = Ο(4Γ9) = Ο(4)Ο(9) = 2Γ6 = 12 Since gcd(5,36)=1, Eulerβs theorem: 512 β‘ 1 (mod 36) Now 123 = 12Γ10 + 3 5123 β‘ (512)10 Γ 53 β‘ 110 Γ 125 β‘ 125 (mod 36) 125 Γ· 36 = 3Γ36 = 108, remainder 17 Answer: remainder = 17.
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