RU-ALLRUSSIAN 1972 Problem 4

a, m, n are positive integers and a $>1$ . Show that if $\mathrm{a^{m} + 1}$ divides $\mathrm{a^{n} + 1}$ , then m divides n. The positive integer b is relatively prime to a, show that if $\mathrm{a^{m} + b^{m}}$ divides $\mathrm{a^{n} + b^{n}}$ then m divides n.