Problem #408

Sum of three cubes
Public 07/14/17 7xp Programming 56.3%

It is conjectured that all positive integers, not of the form $9 \times k \pm 4$ can be written as a sum of 3 cubes, probably in infinitely many ways.

Some decompositions are hard to discover.

For instance, the smallest decomposition of 74 was only discovered in 2016:
$ 74 = -284650292555885^3 + 66229832190556^3 + 283450105697727^3 $

Decompositions for all integers up to 100 are known, except for 33 and 42.

Find all the decompositions of 1026 where the absolute value of each cube is $\lt 10^5$.

Answer format: $ Count,X,Y,Z \textrm{ where } X \lt Y \lt Z$ is the triple with the largest absolute values for X

You are given : 6,-14900,10849,12664 for 993 and a threshold of 20000.

$993 = -14900^3+10849^3+12664^3$
$993 = -11450^3-4127^3+11626^3$
$993 = -8339^3+6121^3+7051^3$
$993 = -2528^3+673^3+2512^3$
$993 = -1007^3-842^3+1174^3$
$993 = -2^3+1^3+10^3$

[My timing: 60 sec]



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