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Proof pearl: Bounding least common multiples with triangles


Joseph Chan and Michael Norrish

Australian National University



We present a proof of the fact that 2^n ≤ lcm{1 . . . (n + 1)}. This result has a standard proof via an integral, but our proof is purely number theoretic, requiring little more than list inductions. The proof is based on manipulations of a variant of Leibniz’s Harmonic Triangle, itself a relative of Pascal’s better-known Triangle.

BibTeX Entry

    author           = {Chan, Joseph and Norrish, Michael},
    editor           = {{Jasmin Christian Blanchette and Stephan Merz}},
    month            = aug,
    year             = {2016},
    title            = {Proof Pearl: Bounding Least Common Multiples with Triangles},
    address          = {Nancy, France},
    pages            = {140--150},
    booktitle        = {International Conference on Interactive Theorem Proving},
    paperurl         = {},
    publisher        = {Springer},
    slides           = {/publications/nicta_slides/9267.pdf},
    isbn             = {9783319431437}