MathDB

Let a sequence

\{a_n\}

n \in \mathbb{N}^{*}

given, satisfying the condition

0 < a_{n+1} - a_n \leq 2001

for all

n \in \mathbb{N}^{*}

Show that there are infinitely many pairs of positive integers

(p, q)

such that

p < q

and

a_p

is divisor of

a_q

N4