Do there exist pairs of distinct real numbers whose arithmetic, geometric and harmonic means are all integers? – math.stackexchange.com

Do there exist pairs of distinct real numbers whose arithmetic, geometric and harmonic means are all integers? – math.stackexchange.com

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I self-realized an interesting property today that all numbers $(a,b)$ belonging to the infinite set $$\{(a,b): a=(2l+1)^2, b=(2k+1)^2;\ l,k \in N;\ l,k\geq1\}$$ have their AM and GM both integers. ...

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