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Posts for July 2012.

We show how Partial Fraction Decomposition is a consequence of the Chinese Remainder Theorem. Our results hold for arbitrary principal ideal domains, with stronger results for certain Euclidean rings. Therefore, we do not only have Partial Fraction Decomposition for rational function fields, but also for the rational numbers.
In this post, we derive an explicit lower bound for the number of pairs of coprime integers bounded by some n.