For every positive integer n we take the greatest divisor d of n such that d≤√n and we define an=nd−d. Prove that in the sequence a1,a2,a3,..., any non negative integer k its in the sequence infinitely many times.
Source: 2023 Mathematics Regional Olympiad of Mexico West P1
Tags: number theory, divisor
For every positive integer n we take the greatest divisor d of n such that d≤√n and we define an=nd−d. Prove that in the sequence a1,a2,a3,..., any non negative integer k its in the sequence infinitely many times.