What is a modern version of Archimedes's cattle problem? A problem which will require 2,000 years to solve.
Part I of the cattle problem was a set of linear Diophantine equations; Part II added quadratic Pell-equation constraints. A modern extension might add cubic elliptic-curve constraints.
Alternatively, factoring F12 will probably take on the order of 2000 years.
update: "An unusual cubic representation problem" by Andrew Bremner and Allan MacLeod.
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