Question 69
Let $a_1, a_2, \dots, a_{41}$ be an arithmetic sequence such that
$$
\frac{1}{\sqrt{a_1} + \sqrt{a_2}} + \frac{1}{\sqrt{a_2} + \sqrt{a_3}} + \dots + \frac{1}{\sqrt{a_{40}} + \sqrt{a_{41}}}
$$
is a positive integer. If $a_1 = 1$, and the common difference of the sequence is a positive integer, find the common difference.
*(Anastazija Pažanin)*
$$
\frac{1}{\sqrt{a_1} + \sqrt{a_2}} + \frac{1}{\sqrt{a_2} + \sqrt{a_3}} + \dots + \frac{1}{\sqrt{a_{40}} + \sqrt{a_{41}}}
$$
is a positive integer. If $a_1 = 1$, and the common difference of the sequence is a positive integer, find the common difference.
*(Anastazija Pažanin)*