4 replies on “Math From Scratch 15: The Fundamental Theorem of Arithmetic”

  1. StarDrifter says:

    I’m enjoying this series. I’m a bit confused by the following statement though

    As an example, let us prove that if p is prime, and if a1, a2, …, an are integers, then there exists at least one i for which p divides ai.

    Am I missing some other constraint on these variables? What if I pick p = 7, n = 3, a1 = 1, a2 = 2, and a3 = 3?

    • No, I missed listing the constraint. It should read that, if p divides the PRODUCT of all n integers, then p must divide one of the integers on the list. I’ll get that corrected and reposted this week.

      • StarDrifter says:

        While on the topic of corrections, should “the result follows from the assumption of the n + 1 case” refer to the case for “n” and not “n + 1”?

  2. Thanks for catching those. Both errors should now be corrected.

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