Statement about factorials that I don't understand

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SUMMARY

The statement "If t > 2n^2 is an integer, then t! > (n^2)^(t-n^2)" is a mathematical assertion that can be proven using algebraic techniques. The discussion suggests that the proof may also involve advanced concepts such as the gamma function or Stirling's approximation. Participants recommend exploring mathematical induction as a method for establishing the validity of this statement. Understanding these concepts is crucial for grasping the underlying principles of factorial growth in relation to polynomial expressions.

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  • Understanding of factorial notation and properties
  • Familiarity with algebraic manipulation
  • Basic knowledge of the gamma function
  • Concepts of Stirling's approximation
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Ertosthnes
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I was reading and came across this statement:

If t > 2n^2 is an integer, then t! > (n^2)^(t-n^2)

I'm not sure why it is true. I don't know what equations are relevant. My feeling is that you don't need anything more than algebra, but perhaps it would also follow from the gamma function or stirling's formula. Can anyone help me out?
 
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Have you tried to prove it by induction?
 

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