1

I'm looking for the complete proof (in a textbook preferably) of harmonic number $H_n$ denominator being divisible by all primes $p\in\left[\frac{n+1}{2},n\right]$.

I found one by induction in Exploring Euler's Constant by Julian Havil. However, I find it lacking because no reasoning is given why the left part of the interval $\frac{n+1}{2}$ moves too. As I see it, induction step explains the addiction of new primes only.

TheGrandDuke
  • 351
  • 2
    Isn't this obvious? Any prime in that range appears in exactly one denominator, hence can't be cancelled when you add the fractions. – lulu Aug 11 '21 at 13:38
  • If you want us to critique the proof, you should show us the proof, or at least the part of it you're calling into question. – saulspatz Aug 11 '21 at 13:51
  • @lulu Of course, but it doesn't stem from the induction as Havil presents it (or I see it). I'm looking proof for the reference purposes and I want everything explained in one place.

    P.S. saulspatz The critique of Navil proof is not the goal.

     – TheGrandDuke Aug 11 '21 at 14:00
  • I don't understand. The proof is obvious. If you want the argument to align with some other proof (or sketch), you should provide the other argument. – lulu Aug 11 '21 at 14:04

0 Answers0