Triplet Pairs

Ans 5

@just_neelansh
ab=c
bc=a
ca=bhence $a_{2}b_{2}c_{2}=abc$
case 1: abc=0 > (0,0,0)case 2 abc=1,
infinite?? should it not be integers??

@nukitapuyol
me too think same.

@ashishdeosingh @nukitapuyol
i checked it, the given answer is 5
Sorry, its also given that no two of them are same.

@just_neelansh
no two same means all a,b,c different?

@ashishdeosingh think so, i updated the question you can check there

@just_neelansh
need not be pairwise distinct means two of them can be same??

@ashishdeosingh need not be pairwise distinct means two numbers can be same. Even all three can be same. But in the bracket the question is telling no two of them are same. How can it be possible? Arent they exact opposite sentences?

@harshalpatil
exactly.

to be sure ,
you need ab=c, bc=a,ca=b we have two trivial solutions (0,0,0) and (1,1,1) only

@nukitapuyol
even (1,1,1)
(1,1,1)
(1,1,1) are solutions

@ashishdeosingh this means (0,0,0),(1,1,1),(1,1,1),(1,1,1),(1,1,1) are the solutions..

@tusharrathore
what else can this mean?

@ashishdeosingh why had they written "no two of them are same".?? From this ∞ solutions are possible ...

@tusharrathore
how do i know? as @HarshalPatil pointed last line of your question made it ambigous.