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Proof Pearl: Bounding Least Common Multiples with Triangles

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We present a proof of the fact that for $$n \ge 0$$n≥0. This result has a standard proof via an integral, but our proof is purely number-theoretic, requiring little more… Click to show full abstract

We present a proof of the fact that for $$n \ge 0$$n≥0. This result has a standard proof via an integral, but our proof is purely number-theoretic, requiring little more than inductions based on lists. The almost-pictorial proof is based on manipulations of a variant of Leibniz’s harmonic triangle, itself a relative of Pascal’s better-known Triangle.

Keywords: pearl bounding; bounding least; common multiples; proof; proof pearl; least common

Journal Title: Journal of Automated Reasoning
Year Published: 2017

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