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Decomposition of Numbers into Prime Factors
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addition adjacent fractions algebraic number angle application approximation automorphic function belong circle of radius clearly combined common multiple complex numbers continued fraction convergent coprime cyclic group decimal fraction decomposed denominator divided divisible divisor elements equal Euclid's lemma example fact Farey sequence figure finite number fixed points Ford circles formula fundamental region geometry Hence hinges identity inequality infinite group infinity integers interior intersection interval invariant inversion with respect irrational number isometric circles linear transformations linkage mathematics matrix mediant mesh modular group modular substitution modular transformation norm number of objects original pair parallelogram Pell's equation pigeon-hole principle point of tangency polynomial positive prime factors prime numbers problem proof prove rational numbers real axis reciprocal reduced fraction remainder rhomboid satisfied sequence of order solution straight line sub-group Suppose Sylvester's formula tangent theorem theory unit circle upper half plane x-axis zero