September 5th, 2019, 10:26 AM  #1 
Senior Member Joined: Dec 2015 From: somewhere Posts: 642 Thanks: 91  3 variable equations
Solve for positive integers : $\displaystyle x+y+z=xyz$ . Method required ! 
September 5th, 2019, 12:18 PM  #2 
Senior Member Joined: Jun 2019 From: USA Posts: 213 Thanks: 90 
Wait, did my post not post? Grrr. Let x <= y <= z. x+y+z<=3z, thus xy<=3, thus x<=sqrt(3), thus x=1. 1+1+z=z doesn't work, so y=2 or y=3. Yada yada, something about the Jackson 5, and there's your answer! (Engineering method: Had MATLAB probe [1,100]^3, found 6 answers. Bada bing, bada boom!) 

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