The p-adics form an infinite collection of number systems based on prime numbers. They’re at the heart of modern number theory.
Think of a two sides, three sided, five sided coins. the number of sides on our dice corresponds to the number of binomials needed moment balancing. The mathematicians know more than they are willing to prove at the moment, and I am just a blogger. But the connections between Markov n-tuple trees and p-adics is intimate and will form a 'relative prime' theory of numbers. The connection is via continued fractions.
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