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so weamp;#39;ve seen now how the magic equation for tricolor ability gives us a computational tool for determining whether a given knot has a tri coloration and if it does have a tri coloration how many tri colorations does it have this seems like it could be a really powerful way to distinguish between different types of knots the limitation that it has though is that it only uses three colors and tri coloration might not be enough to distinguish between knots in general we may need to use four colors or five or seven or 12 or 18 or 212 right what weamp;#39;d like to do is push the envelope a little bit and figure out how to go from a tri color ability condition into aka color ability condition if I have K colors to work with how do I come up with a new magic equation which I can then use to build a square system of linear equations that I can then use modular arithmetic to determine whether or not solutions exist for that K coloration system of equations this is going to be ultimat