MathDB

(a_{n})_{n=1}^{\infty}

is an integer sequence,

a_{1}=1

a_{2}=2

and for

n\geq{1}

a_{n+2}=a_{n+1}^{2}+(n+2)a_{n+1}-a_{n}^{2}-na_{n}

a)

Prove that the set of primes that divides at least one term of the sequence can not be finite.

b)

Find 3 different prime numbers that do not divide any terms of this sequence.

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