Given a repunit Rn, show that Rn can be divided by 11 if and only if n is even.    

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justaguide eNotes educator| Certified Educator

You can ask only one question at a time. I have edited your question accordingly.

A repunit is a number that has only 1 as its digits. Rn is a number that has n 1s.

A number is divisible by 11 if the difference of the sum of the even-placed digits and the sum of the odd-placed digits is divisible by 11 or equal to 0.

For a repunit, this is true only if the number of digits is even as then adding and subtracting alternate digits would give a result of 0. If n is odd, the same would be equal to 1.

This proves that for a repunit Rn, the number is divisible by 11 only if if n is even.

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