vicentev 23.10.2024 17:41 Determine all triples \( (a, b, c) \) of positive integers such that: \[ a + b + c = abc. \]
Nuran2010 23.10.2024 20:02 Let's say WLOG $a\geq b \geq c$.So,$abc=a+b+c<=3a$.$a\neq0$ so,$3 \geq bc$.Rest is to check $c=1,b=1,2,3$.From,$a+b+c=abc$,we have:$a|a+b+c\Rightarrow a|b+c$ and analogously same for others,so permutations of $(1,2,3)$ are the solutions.