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It is obviously true that

FactorialPower[k, m] <= k^m

when k and m are both positive integers.

Is there anyway to verify this in Mathematica?


Note, initially I mistakenly used Pochhammer instead of FactorialPower

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  • $\begingroup$ It is false in view of Pochhammer[k, m]/k^m /. {k -> 234, m -> 137} // N which produces $ 4.57254\times 10^{14}$. $\endgroup$ – user64494 Oct 31 '19 at 13:01
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    $\begingroup$ Use FindInstance to find a counterexample: FindInstance[{Pochhammer[k, m] > k^m, k > 0, m > 0, Element[{m, k}, Integers]}, {k, m}] $\endgroup$ – Bob Hanlon Oct 31 '19 at 14:34
  • $\begingroup$ @ Bob Hanlon : The opposite inequality is Pochhammer[k, m] >= k^m. $\endgroup$ – user64494 Oct 31 '19 at 16:03
  • $\begingroup$ @user64494 - Yes, but either will provide a counterexample. $\endgroup$ – Bob Hanlon Oct 31 '19 at 16:25
  • $\begingroup$ FactorialPower[k,1]==k^1 $\endgroup$ – mikado Oct 31 '19 at 20:15

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