Quadratic Residue Mystery Cache
Hidden : 10/4/2013
Difficulty:
2.5 out of 5
Terrain:
2.5 out of 5

Size: Size: regular (regular)

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Geocache Description:

This geo-art consists of twenty-six Unknown/Mystery caches which each have a puzzle to solve in order to determine the coordinates of the final location (a container with log book and in most cases some swag). The final location may be a park & grab along a graded forest road (accessible with a 2WD car), a reasonably short hike or drive up a Jeep trail (may require 4WD or a high ground-clearance vehicle), or a short hike up a foot trail.


In number theory, an integer q is called a quadratic residue modulo n if it is congruent to a perfect square modulo n; i.e., if there exists an integer x such that: x2 ≡ q (mod n)

For a given n a list of the quadratic residues modulo n may be obtained by simply squaring the numbers 0, 1, …, n − 1. Because a2 ≡ (n − a)2 (mod n), the list of squares modulo n is symmetrical around n/2, and the list only needs to go that high.

Thus, the number of quadratic residues modulo n cannot exceed n/2 + 1 (n even) or (n + 1)/2 (n odd).

The product of two residues is always a residue.


You'll find the location of the cache by using the following image:

Additional Hints (Decrypt)

dhvpx erfcbafr

Decryption Key

A|B|C|D|E|F|G|H|I|J|K|L|M
-------------------------
N|O|P|Q|R|S|T|U|V|W|X|Y|Z

(letter above equals below, and vice versa)


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