\$230.\$ (April, 1915) Proposed by E. B. Escott, Ann Arbor, Michigan - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-19T18:28:26Z http://mathoverflow.net/feeds/question/54862 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/54862/230-april-1915-proposed-by-e-b-escott-ann-arbor-michigan \$230.\$ (April, 1915) Proposed by E. B. Escott, Ann Arbor, Michigan Luis H Gallardo 2011-02-09T08:41:48Z 2011-02-10T08:21:21Z <p>Just browsing some old stuff in my office for other thing I found the following:</p> <p>\$230.\$ (April, 1915) Proposed by E. B. Escott, Ann Arbor, Michigan.</p> <p>Find three numbers such that their sum, the sum of their squares, and the sum of their cubes , shall be a cube.</p> <p>Note.--W. D. Cairns says this problem, which was proposed in <code>L'Intermediaire</code> in \$1900\$, remains unsolved to date, even though it was reprinted in February, \$1913\$.</p> http://mathoverflow.net/questions/54862/230-april-1915-proposed-by-e-b-escott-ann-arbor-michigan/54875#54875 Answer by Tapio Rajala for \$230.\$ (April, 1915) Proposed by E. B. Escott, Ann Arbor, Michigan Tapio Rajala 2011-02-09T12:14:15Z 2011-02-09T12:14:15Z <p>With a quick search from the internet I was able to only find the solution \$\$(146, -1314, 1168)\$\$ by <strong>E. T. Bell</strong> in <em>The American Mathematical Monthly</em>, Vol. 24, No. 5 (May, 1917), p. 240. The paper can be found from <a href="http://www.jstor.org/stable/pdfplus/2974328.pdf" rel="nofollow">http://www.jstor.org/stable/pdfplus/2974328.pdf</a></p> <p>(Also, a quick computer search shows that there are no positive solutions with the largest integer being less than 90000.)</p>