MathDB

Algebra and NT

Source:

February 12, 2022

Sequencesalgebranumber theoryKvant

Problem Statement

Let

a_1,a_2, \cdots

be a sequence of integers that satisfies:

a_1=1

and

a_{n+1}=a_n+a_{\lfloor \sqrt{n} \rfloor} , \forall n\geq 1

. Prove that for all positive

k

, there is

m \geq 1

such that

k \mid a_m

.