SOLUTION: Are there m, n, k so that: 1/m + 1/n + 1/k = 1/(m+n) + 1/(n+k) + 1/(m+k) ?

Question 1019023: Are there m, n, k so that:
1/m + 1/n + 1/k = 1/(m+n) + 1/(n+k) + 1/(m+k) ?
Answer by ikleyn(52776) (Show Source): You can put this solution on YOUR website!
.
Are there m, n, k so that:
1/m + 1/n + 1/k = 1/(m+n) + 1/(n+k) + 1/(m+k) ?
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First addend in the right side is LESS than first addend in the left side.

Second addend in the right side is LESS than second addend in the left side.

Third addend in the right side is LESS than third addend in the left side.

Hence, what?

Hence, this equation does not have solutions in positive numbers.

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