Proof Pearl: Bounding Least Common Multiples with Triangles

摘要

We present a proof of the fact that for n0. 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.