Prove that (n) is divisible by (n)^(n-1)

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SUMMARY

The discussion centers on proving that (n!)! is divisible by (n!)^(n-1)!. Initial explorations with n=2, n=3, and n=4 reveal patterns in factorials, specifically (2!)! = 2! and (3!)! = 6!. Participants suggest employing mathematical induction as a method for proof and inquire about familiarity with multinomial coefficients, indicating their relevance in the proof process.

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  • Understanding of factorial notation and properties
  • Familiarity with mathematical induction techniques
  • Knowledge of multinomial coefficients
  • Basic combinatorial mathematics
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  • Study mathematical induction proofs in combinatorial contexts
  • Research multinomial coefficients and their applications
  • Explore advanced properties of factorials and their divisibility
  • Practice problems involving divisibility of factorial expressions
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Mathematicians, students studying combinatorics, and anyone interested in advanced factorial properties and proofs.

sothea hoeung
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Prove that (n!)! is divisible by (n!)^(n-1)!
 
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first try playing with n=2 then n=3 then n=4 and see if you can find a pattern and only evaluate the n! itself not everything to see the pattern

(2!)! = 2! and (3!)! = 6! and (4!)!=24! vs (2!)^(1!)= 2^1 ...

Next I think you need to use induction to prove it.
 


Are you familiar with multinomial coefficients??
 

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