Problem

Source: Indian TST D1 P2

Tags: number theory



Show that there do not exist natural numbers $a_1, a_2, \dots, a_{2018}$ such that the numbers \[ (a_1)^{2018}+a_2, (a_2)^{2018}+a_3, \dots, (a_{2018})^{2018}+a_1 \]are all powers of $5$ Proposed by Tejaswi Navilarekallu