So nkurz is correct that, in the paper, N is always equal to the maximum bitwidth of the numerator. I was not careful enough to make sure that the notation of the paper matches the notation of the blog post. So the N from the blog post is the F from the paper. I am sorry about this.
I added the following footnote.
"What is N? If both the numerator n and the divisor d are 32-bit unsigned integers, then you can pick N=64. This is not the smallest possible value. The smallest possible value is given by Algorithm 2 in our paper and it involves a bit of mathematics (note: the notation in my blog post differs from the paper, N becomes F)."
To make it super simple, if you have 32-bit values, then pick N (from the blog post) to be 64 and you are all set. You can do better, but this requires knowing what the divisor is.
I'm one of the co-authors, and I believe that in our case, N is always equal to the maximum bitwidth of the numerator. So for a 32-bit integer, N=32. I'll see if Daniel can add some clarification to the blog post.