2I need help with this puzzle, I tried to solve it but could find what's wrong with my solution, forgive me if I have any silly mistakes. it has been quite some time since I have done any mathematics.The Puzzle: A natural number n is a rotor if and only if the decimal representation of n+n is the same as a rotation of the decimal representation of n in which the last digit has been moved to the front. In other words, the decimal representation n1 n2 ... nk-1 nk satisfies the following sum.n1 n2 ... nk-1 nk+ n1 n2 ... nk-1 nk____________________________nk n1 ... nk-1What is the smallest rotor?I started by the following:because n1 = nk2nk2and ny = nk2∗ynk2∗y ----> (1)and because nk = nk−12nk−12 ---->(2)from (1) and (2)nk = nk2∗knk2∗k = nk4∗(k−1)nk4∗(k−1)can't I from nk = nk2∗knk2∗k infer that k = 1/2 ?and can't I from nk2∗knk2∗k = nk4∗(k−1)nk4∗(k−1) infer that k = 2 ?I don't understand what I am doing wrong, any help please ? and what is the proper solution to the original problem ? thanks a lot