Project Euler Problem 440 – GCD and Tiling

Spoiler Alert! This blog entry contains content that might help you solve problem 440 of Project Euler. Please don’t read any further if you have yet to attempt to solve the problem on your own. The information is intended for those who failed to solve the problem and are looking for hints. It is posted not before the problem has a hundred solvers already.

Test Data

T(99) mod 987898789184312344
T(12345678910101213) mod 987898789246963623
gcd(T(73), T(711)) mod 98789878910610040
$\sum_{a=1}^{2000}\sum_{b=1}^{2000} \text{gcd}(T(1848^a),T(1848^b))$ mod 987898789560367075