Here is a good problem if anyone wants to give it a go.
Find the smallest positive integer such that when the first digit is shifted to the end, the result is 3/2 times the original number.
For instance, 1284 becomes 2841. But 2841 is not 3/2 times 1284.
Fermat's Little Theorem may come in handy.
But, feel free to do it however you like.