show (n^2)! is divisible by (n!)^n+1(adsbygoogle = window.adsbygoogle || []).push({});

base case 1 divides 1

so I did the induction and got

(n^2+2n)!=((n+1)^n * (n!) *(n!)^n+1

(n^2+2n)*.......*(n^2)!=((n+1)^n * (n!) *(n!)^n+1

can we conclude that (n^2)! is divisible by (n!)^n+1 for all n from there because we have the bold terms on both sides?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Induction Division

**Physics Forums | Science Articles, Homework Help, Discussion**