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

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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.