MathDB

a_n = n if strictly increasing, a_n<=n+2020m , n^3a_n-1 divisible by a_ {n+1}

Source: SRMC 2020 P1 - Silk Road

August 18, 2020

numberr theoryinequalitiesdivisibledivides

Problem Statement

Given a strictly increasing infinite sequence of natural numbers

a_1,

a_2,

a_3,

\ldots

. It is known that

a_n \leq n + 2020

and the number

n ^ 3 a_n - 1

is divisible by

a_ {n + 1}

for all natural numbers

n

. Prove that

a_n = n

for all natural numbers

n