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

AI Thread Summary
The statement (mn)! = m!n! for positive integers m and n is false, as demonstrated by the example (3*2)! = 720, which does not equal 3!2! = 12. The discussion also touches on proving that the square root of a prime integer is irrational, suggesting a proof by contradiction approach. The initial poster expresses confusion and seeks assistance with both mathematical claims. Additionally, a suggestion is made to post homework questions in a dedicated forum for better responses. The conversation highlights the importance of verifying mathematical identities and seeking help in appropriate channels.
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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?
 

Thread 'Formal derivation of statement from Peano Arithmetic system'

I was reading a Bachelor thesis on Peano Arithmetic (PA). PA has the following axioms (not including the induction schema): $$\begin{align} & (A1) ~~~~ \forall x \neg (x + 1 = 0) \nonumber \\ & (A2) ~~~~ \forall xy (x + 1 =y + 1 \to x = y) \nonumber \\ & (A3) ~~~~ \forall x (x + 0 = x) \nonumber \\ & (A4) ~~~~ \forall xy (x + (y +1) = (x + y ) + 1) \nonumber \\ & (A5) ~~~~ \forall x (x \cdot 0 = 0) \nonumber \\ & (A6) ~~~~ \forall xy (x \cdot (y + 1) = (x \cdot y) + x) \nonumber...
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