MathDB

Let

\operatorname{rad}(k)

denote the product of prime divisors of a natural number

k

(define

\operatorname{rad}(1)=1

). A sequence

(a_n)

is defined by setting

a_1

arbitrarily, and

a_{n+1}=a_n+\operatorname{rad}(a_n)

for

n\ge1

. Prove that the sequence

(a_n)

contains arithmetic progressions of arbitrary length.

Problem Statement