This thesis focuses on a function which moves the last digit of an integer to the first position, e.g. A(123) = 312. The objective of this thesis is to show how one can find all solutions x to the equation A(x)  = kx, where k is a rational number. It also explains the connection between the solutions and certain periodic decimal numbers, and in which way these decimal numbers can be used to solve the equation. Finally, the problem is generalized to other bases than 10.