MathDB

a_{b_n} is arithmentic progression , b_n | b_{n+1}

Source: 2020 Colombia day 2 p1

November 27, 2022

arithmetic sequencedividesnumber theory

Problem Statement

Find all of the sequences

a_1, a_2, a_3, . . .

of real numbers that satisfy the following property: given any sequence

b_1, b_2, b_3, . . .

of positive integers such that for all

n \ge 1

we have

b_n \ne b_{n+1}

and

b_n | b_{n+1}

, then the sub-sequence

a_{b_1}, a_{b_2}, a_{b_3}, . . .

is an arithmetic progression.