MathDB

Let

a_1,a_2,a_3,\cdots

be the sequence of positive integers such that

a_1=1 , a_{k+1}=a^3_k+1,

for all positive integers

k.

Prove that for every prime number

p

of the form

3l +2,

where

l

is a non-negative integer ,there exists a positive integer

n

such that

a_n

is divisible by

p.

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