Team Yofa: This area seems too unstable for resilient cache hides, so I'm going to archive this one. As always, here's the solution:
The puzzle is based on the Diffie-Helman algorithm, a way of sharing a secret between two people even when their communications are being observed.
First, Cheezburger Cat needs to pick a secret integer that he keeps to himself and never shares. He decides to use pi. He can only use as many digits of pi as will fit in the group (meaning smaller than the modulus). The modulus prime number was arbitrarily picked by Cheezburger Cat to be 1234567898765437 (the smallest prime greater than 1234567898765432). This means he can use 15 digits of pi, which is 314159265358979. Alpha (also known as g) is 6 (chosen by Cheezburger Cat because 6 is a generator of the multiplicative group of integers modulo 314159265358979). Cheezburger Cat typed "6^314159265358979 mod 1234567898765437" into www.wolframalpha.com and gets 896316645004725, which he tells TacocaT.
Now TacocaT needs to pick a secret integer to keep to himself as well. He uses 15 digits of e. Using www.wolframalpha.com, TacocaT computes 6^271828182845904 mod 1234567898765437 to get 168907200925645, and tells this number to Cheezeburger Cat.
Now, Cheezeburger Cat can computer 168907200925645^314159265358979 mod 1234567898765437, and TacocaT can compute 896316645004725^271828182845904 mod 1234567898765437, and through the magic of Diffie-Helman, they both get the same answer, 951240594088466. No one watching the communication could know the secret number, even through they heard every word the cats exchanged.
Now, 576944781944041 is subtracted from the shared secret, and out pops the coordinates: 374295812144425, or N37 42.958, W121 44.425 :-)