Problem 168

Number Rotations

Consider the number 142857. We can right-rotate this number by moving the last digit (7) to the front of it, giving us 714285.

It can be verified that 714285=5142857.

This demonstrates an unusual property of 142857: it is a divisor of its right-rotation.

Find the last 5 digits of the sum of all integers `n`, 10 `n` 10^{100}, that have this property.

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