blackpenredpen

math for fun 

To see this working, head to your live site.
  • Categories
  • All Posts
  • My Posts
Setsuna Kujo
Aug 17, 2021

Primes, Factorials, and Troll math

in Math Problems

I was watching flammable maths' video on ambiguous math trolls, specifically one involving ratios (No, not the twitter ratios) and factorials. He stated:


25 - 5 : 5 = 4!

721 - 103 : 103 = 6!


Where the ! mark at the end could either be the factorial symbol or just an exclamation mark. He then derived:


For a - b : b = k! (k! in the sense of the riddle)

a = k! + 1 (real factorial this time)

b = (k! + 1)/(k + 1) [again, real factorial]


He then concluded that k must be even since if it were odd then we would wind up with odd/even which isn't a whole number.


By similar logic I found out that k+1 must be prime because if it weren't then k!+1 wouldn't divide k+1.


I did some experimenting and tested prime k+1 until 19 and it turns out all the prime values of k+1 work.


So my question is: do all prime numbers P follow the property that p divides (p-1)! + 1?

1 answer0 replies
0
2
Ian Fowler
Aug 17, 2021

en.wikipedia.org
Wilson's theorem - Wikipedia

1 comments