- Thread starter
- #1
Albert
Well-known member
- Jan 25, 2013
- 1,225
$a,b,c \in N$
(1) $1<a<b<c$
(2)$(ab-1)(bc-1)(ca-1) \,\, mod \,\, (abc)=0$
$find :a,b,c$
(1) $1<a<b<c$
(2)$(ab-1)(bc-1)(ca-1) \,\, mod \,\, (abc)=0$
$find :a,b,c$
max value is not 1 \(\displaystyle its \frac{13}{12}\).....has a maxmum value of 1.....
yes (2,3,5) is the only solution..,but how to get the answer ?But,I guess (2,3,5) is the only solution....![]()
very nice solutionIn,
\(\displaystyle \frac{1}{a}+\frac{1}{b}+\frac{1}{c}=1+\frac{1}{abc}\)
L.H.S to be greater than one (a,b) should be (2,3) substituting them rest is linear equation
\(\displaystyle \frac{1}{2}+\frac{1}{3}+\frac{1}{c}=1+\frac{1}{6c}\)
\(\displaystyle c=5\)