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Divisible By 11

Problem

Consider the following results.

101 + 1 = 11
102 minus 1 = 99 = 9 times 11
103 + 1 = 1001 = 91 times 11
104 minus 1 = 9999 = 909 times 11
105 + 1 = 100001 = 9091 times 11

Prove that 10nminus1 is divisible by 11 if n is even and 10n+1 is divisible by 11 if n is odd.

Problem ID: 208 (17 Feb 2005)     Difficulty: 3 Star

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