# On Richard Guy's problem D5 in "Unsolved problems in Number Theory"

This question is motivated by recent discovery of Andrew Booker+Andrew Sutherland.

Richard Guy's problem D5 in his Unsolved Problems in Number Theory contains the original question for the sum of three cubes and a few other interesting problems, e.g. the solutions of Diophantine equation $$x^3+y^3+2z^3=k,$$ where $$k$$ is an integer neither a cube nor twice a cube. For $$k<1000$$, only two candidates $$k=148, 671$$ are left(see Tomita Seiji's database).

Question: Is there any known computational effort for these two Diophantine equations?

Above equation shown below:

           $$x^3+y^3+2z^3=K$$ -----$$(1)$$


Allan Macleod has given a method for finding

numerical solutions to equation $$(1)$$.

The link to his article is given below.

    https://arxiv.org/pdf/1109.2396.pdf


If "OP" has done some research on equation $$(1)$$ then

maybe he can post it on "math overflow" website.

That way it may help others to find more numerical

solutions to the unknown values of $$'K'$$ in equation $$(1)$$.