# 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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