Can you prove or disprove (mn)!=m!n! for positive integers m and n?

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Discussion Overview

The discussion centers around the claim that for positive integers m and n, the equation (mn)! = m!n! holds true. Participants are asked to prove or disprove this assertion, as well as to provide assistance on a separate question regarding the irrationality of the square root of a prime integer.

Discussion Character

  • Debate/contested, Homework-related

Main Points Raised

  • One participant asserts that the equation (mn)! = m!n! is true but admits to being unable to prove it.
  • Another participant provides a counterexample, stating that (3*2)! = 720 does not equal 3!2! = 12, thus claiming the equation is false.
  • A third participant expresses surprise at the previous claim and shifts focus to the second question about the irrationality of the square root of a prime integer.
  • A later reply suggests using proof by contradiction to address the second question, proposing that if sqrt(p) = a/b, then...
  • Additionally, the same reply notes that posting in the homework forum may yield more responses for homework-related questions.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the validity of the equation (mn)! = m!n!. There are competing views, with one participant claiming it is true and another providing a counterexample that suggests it is false. The discussion regarding the irrationality of the square root of a prime integer is also ongoing without a definitive conclusion.

Contextual Notes

Participants have not fully explored the implications of the counterexample provided, and there may be additional assumptions or definitions that influence the validity of the claims made. The second question regarding the irrationality of the square root of a prime integer is presented as a separate topic but remains unresolved.

Who May Find This Useful

This discussion may be of interest to students and enthusiasts of mathematics, particularly those exploring factorial properties and the nature of irrational numbers.

thecleric
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If m and n are positive integers, (mn)!=m!n! Prove or disprove.

its so obviously true i can't prove it. anyone help?

-also-

Prove: The square root of a prime integer is an irrational number.

any help?
 
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(3*2)! = 720 =/= 3!2! = 12

So it's actually FALSE.
 
hah wow, that shows how long i haven't slept.

any idea on the 2nd question?
 

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