Prove 2220^{2n +1}+2003²ⁿ⁺¹is divisible by 4005,n  belongs to  N

Let P(n) be the statement given by:

P(n) =  2220^2n +1+2003²ⁿ⁺¹

In order to prove P(n) is divisible by 4005, we will first verify P(1) as: 

P(1) =  2220^2(1) +1+2003²⁽¹⁾⁺¹

⇒ P(1) =  2220³ + 2003³

⇒ P(1) =  10941048000 + 8036054027 = 18977102027 which is not completely divisible by 4005.

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