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Does there exist a positive integer triad (a,b,c) such that a/b + b/c + c/a =2017/1000. If so, give at least one example. I tried solving this using AP-GP-HP inequality but get some complex thing. Please help me.

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    what can you say by reasoning on denominators ? – 2017-01-11
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    What does this have to do with sequences and series? – 2017-01-11

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The minimum of $f(a,b,c) = a/b + b/c + c/a$ for $a, b, c > 0$ is on $a=b=c$, where $f(a,a,a) = 3$. Since this is greater than $2017/1000$, there are no solutions.

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    Well I have another method...I have posted it....If u could just see it once and judge it...It would be nice. Thank u. – 2017-01-12
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Applying AM-GM inequality We get, ((abc)/(bca))^1/3 ≤ ((a/b) + (b/c) + (c/a))/3

1 ≤ ((a/b) + (b/c) + (c/a))/3

3≤ (a/b) + (b/c) + (c/a)

But since 2017/1000< 3 Therefore there does not exist any such triad.