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Every rational r is xyz(x+y+z) for some rational x,y,z. Proof: Euler (1749) found x(r),y(r),z(r). Nobody knows how.
I have a guess. http://www.math.harvard.edu/~elkies/euler_14t.pdfhttps://people.math.harvard.edu/~elkies/euler_14t.pdf
I have a guess. http://www.math.harvard.edu/~elkies/euler_14t.pdf
I have a guess. https://people.math.harvard.edu/~elkies/euler_14t.pdf