Question 1205493
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Solve : x! × y! = 120 × (xy)!
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<pre>
There are two solutions.



One solution is     x= 5, y= 0.   

Other solution is   x= 0, y= 5.   



Let's prove first that  x= 5, y= 0 is the solution.



Indeed, then  x! = 5! = 120;

              y! = 0! = 1   ( by the definition of 0! )

        thus left side is  x! * y! = 120 * 1 = 120.



Next, for the right side  (xy)! = (5*0)! = 0! = 1 ( again, by the definition of 0! ),

and thus left side, 120, is equal to the right side, which is 120, too.



For other solution, x= 0, y= 5,  the proof is symmetric.
</pre>

Solved.


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Edwin, 


thanks for this valuable addition.

Happy new year!