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00:48
@petaarantes I have edited the answer for now. Please check. Will wait for Anonymous to respond / post an answer.
 
10 hours later…
11:07
@Math Lover OK, let me try to answer this question. But
I think your answer is pretty good and your upper bound is stronger than mine!
 
5 hours later…
15:55
@MathLover If you've delete the answer, may I express your idea (the upper bound) in my answer?
 
4 hours later…
19:27
@Anonymous +1 for your answer. btw an upper bound that shows OP + OQ + OR < 3 is sufficient to prove there are no integer solutions.
btw how do you conclude in your answer that OP + OP' < PQ?

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