Is it true that any monic polynomial of degree 6 with complex coefficients can be represented as a sum of at most three summands each being the cube of at most quadratic polynomials?
B.Shapiro/Stockholm/
Dear Peter,
this is the simplest case of what is unknown in the area of the so-called Waring problem for polynomials. Waring's original question was about the representation of positive integers as sums of powers of other positive integers.
Dear Professor Breuer,
I am a professional and know well what kind of questions one should put to a broad audience to stimulate people's interest. The question I posed is elementary and unsolved and does not have a long history behind it. It might have an elementary answer (which I could not find). If somebody has any reasonable suggestion about this case, I can easily generalize it to a small theory.
As for the style of questions, my former advisor Professor Vladimir Arnold (the famous one) once said that there is a Russian style of formulating mathematical questions and a French style. The Russian style (which I try to follow) is to formulate a mathematical problem in its simpllest unknown case. The French style is to pose a problem in its maximal generality.
Warmest regards, B.Shapiro
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