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 January 4th, 2014, 12:33 AM #1 Senior Member   Joined: Apr 2012 Posts: 799 Thanks: 1 find solution find solution : $w,x,y,z \in N$ $w!=x!+y!+z!$
 January 4th, 2014, 01:13 AM #2 Math Team     Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory Re: find solution I only find (3, 2, 2, 2) after invoking a numerical search. Perhaps this can be approached by noting that x, y, z < w and / or analysing errors of x, y, z with 1/3 * w / etc...?
 January 7th, 2014, 03:17 AM #3 Senior Member   Joined: Apr 2012 Posts: 799 Thanks: 1 Re: find solution let : $x\leq y\leq z$ we have : $3z!\geq w!\geq (z+1)!$ $\therefore z+1\leq 3$ we get : $x=y=z=2,\,\, and \,\, w=3$

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