MathDB

Problem 5 of Second round

Source: IV International Festival of Young Mathematicians Sozopol 2013, Theme for 10-12 grade

January 22, 2020

number theorySequence

Problem Statement

Determine all increasing sequences

\{a_n\}_{n=1}^\infty

of natural numbers with the following property: for each two natural numbers

i

and

j

(not necessarily different), the numbers

i+j

and

a_i+a_j

have an equal number of distinct natural divisors.