1. The problem statement, all variables and given/known data Algebra I.M. Gelfand, problem 134. You know that x+1/x is an integer. Prove that xn+1/xn is an integer for any n = 1, 2, 3, etc. 2. Relevant equations 3. The attempt at a solution I don't fully understand how the induction below proves anything. (Source) I did attempt the solution, yet kept trying because I ignored similar answers to the one below, thinking I didn't prove anything. I don't get this part: "suppose it holds for all k < n" Isn't that what you are supposed to prove?