# Math From Scratch 15: The Fundamental Theorem of Arithmetic

The fifteenth lesson of the Math From Scratch series, dealing with the Fundamental Theorem of Arithmetic, is available here.

## 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.