THE CACHE IS NOT AT THE LISTED COORDINATES.
I have four friends named Alice, Bob, Quentin and Rebecca, who are logic-puzzle mathematical logicians, a species only found in this kind of puzzle: unlike their real-life counterparts, they can do complicated mental arithmetic in seconds, they see all the logical conclusions of every statement, and they never make mistakes.
A few weeks ago they asked me to test their abilities, so I set them this puzzle:
"I have chosen two numbers A and B. A has 6 digits, B has 4 digits, and they are each N less than a perfect square, where N is the day of the month. B divides into A Q times, with remainder R. I have told A to Alice, B to Bob, the (integer) quotient Q to Quentin and the remainder R to Rebecca. What are the numbers?"
A few minutes later, Logician W said "I know the numbers!"
A few minutes later, Logician X said "Aha. Now I know too!"
A few minutes later, Logician Y said "Wow. Now I also know!"
A few minutes later, Logician Z said "Eureka. Now so do I!"
(W, X, Y and Z are of course Alice, Bob, Quentin and Rebecca again, but not in that order.)
If you knew who said what, you could put the numbers they were given in order W, X, Y, Z and take the first two digits of each as CD, FG, HJ and KL respectively. Then the cache is at
N 51 42.[C+K][K+L][D+G+H] E 000 29.[F+H+K][C+H][F+J]
where you use only the last digit of each sum in brackets.
Updated 2022-09-11: new location. The puzzle is unchanged but the formula has been modified. If you solved before this date, add 0.085 minutes North and 0.390 minutes East to your previous solution.
The coordinates may be slightly out because of tree cover. Please see the spoiler image in the checker.
[Why the title? Well, this cache is a revised, improved, in fact resurrected version of an earlier puzzle GC73B7W Re: fraction, which was sort-of based on representing a fraction as quotient Q and remainder R but didn't work out as I intended.]