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.
$993 = 14900^3+10849^3+12664^3$
$993 = 11450^34127^3+11626^3$
$993 = 8339^3+6121^3+7051^3$
$993 = 2528^3+673^3+2512^3$
$993 = 1007^3842^3+1174^3$
$993 = 2^3+1^3+10^3$
[My timing: 60 sec]
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.
$993 = 14900^3+10849^3+12664^3$
$993 = 11450^34127^3+11626^3$
$993 = 8339^3+6121^3+7051^3$
$993 = 2528^3+673^3+2512^3$
$993 = 1007^3842^3+1174^3$
$993 = 2^3+1^3+10^3$
[My timing: 60 sec]
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