Lovable series

The numbers in the sequence are in the form \[a_n=100+n^2, \quad \forall n\in \mathbb{N}\]

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

Find the maximum value of \(d_n\) as \(n\) ranges through positive integers.


Source: AIME
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