MathDB

Let

a_1,a_2,\cdots

be an infinity sequence of positive integers such that

a_1=2021

and

a_{n+1}=(a_1+a_2+\cdots+a_n)^2-1

for all positive integers

n

. Prove that for any integer

n\ge 2

a_n

is the product of at least

2n

(not necessarily distinct) primes.

P3