isi-entrance 2022 Q23

isi-entrance · India · UGA Number Theory Linear Diophantine Equations
The number of triples $( a , b , c )$ of positive integers satisfying the equation $$\frac { 1 } { a } + \frac { 1 } { b } + \frac { 1 } { c } = 1 + \frac { 2 } { a b c }$$ and such that $a < b < c$, equals:
(A) 3
(B) 2
(C) 1
(D) 0
The number of triples $( a , b , c )$ of positive integers satisfying the equation
$$\frac { 1 } { a } + \frac { 1 } { b } + \frac { 1 } { c } = 1 + \frac { 2 } { a b c }$$
and such that $a < b < c$, equals:\\
(A) 3\\
(B) 2\\
(C) 1\\
(D) 0