Prove 11^10 - 1 is divisible by 100

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Beckett

Mathematics

10 December, 05:10

Prove 11^10 - 1 is divisible by 100

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Malik Berry · Answer 1

Assume 11^10 - 1 = 0 (mod 100) (i. e. 11^10 - 1 is divisible by 100). 11^10 - 1 = 0 (mod 100) 11^10 = 1 (mod 100) (11^2) ^5 = 1 (mod 100) (121) ^5 = 1 (mod 100) (21) ^5 = 1 (mod 100) [the remainder of 121 divided by 100 is 21] (21^2) ^2 (21) = 1 (mod 100) (41) ^2 (21) = 1 (mod 100) 81 (21) = 1 (mod 100) 1701 = 1 (mod 100) ∴ 11^10 - 1 is divisible by 100.