Lovable series

The numbers in the sequence are in the form an=100+n2,nNa_n=100+n^2, \quad \forall n\in \mathbb{N}

For each nn, let dnd_n be gcd(an,an+1)\gcd(a_n,a_{n+1}).

Find the maximum value of dnd_n as nn ranges through positive integers.


Source: AIME
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