The numbers in the sequence 101,104,109,116,… are of the form \(a_{n}=100+n^{2}\), where n=1,2,3,…. For each n, let \(d_{n}\) be the greatest common divisor of \(a_{n}\) and \(a_{n+1}\). Find the maximum value of \(d_{n}\) as n ranges through the positive integers.

(第三届AIME1985 第13题)