perplexus.info :: Just Math : Simultaneous Satisfaction III

Simultaneous Satisfaction III (Posted on 2016-03-21)

Determine all possible triplets (A,B,C) of positive integers that satisfy this system of equations:
A + B/C = B +C/A = C + A/B = 2016

No Solution Yet Submitted by K Sengupta

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Definitely D1 (spoiler)

Comment 1 of 1

In order to be all be integers,

B>= C >= A >= B

So, A = B = C

Therefore, B/C = 1

So the only integral solution is (2015,2015,2015)

Posted by Steve Herman on 2016-03-21 08:42:32

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