Just browsing some old stuff in my office for other thing I found the following:


$230.$ (April, 1915) Proposed by E. B. Escott, Ann Arbor, Michigan.


Find three numbers such that their sum, the sum of their squares, and the sum of their cubes
, shall be a cube.


Note.--W. D. Cairns says this problem, which was proposed in `L'Intermediaire` in $1900$,
remains unsolved to date, even though it was reprinted in February, $1913$.



$230.$ (April, 1915) Proposed by E. B. Escott, Ann Arbor, Michigan
With a quick search from the internet I was able to only find the solution $$(146, -1314, 1168)$$ by **E. T. Bell** in *The American Mathematical Monthly*, Vol. 24, No. 5 (May, 1917), p. 240. The paper can be found from <http://www.jstor.org/stable/pdfplus/2974328.pdf>


(Also, a quick computer search shows that there are no positive solutions with the largest integer being less than 90000.)


