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Congruencies, unites modulo n, lattices and abelian groups, quadratic residues, arithmetic functions, Diophantine equations, Farey fractions, continued fractions, partition function, the Sieve method, density of subsets of integers, c-function, the prime number theorem. Some simple examples exist from maps of the interval $[0,1]$ (with addition modulo 1), where these questions can be answered, but more general groups, they are open. Wolff: Binary Universe - The Binary Nature of Reality (Waves form from two balanced forces, Spherical In-Waves and Out-Waves).

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