x^3 + y^3 + z^3 ± (x+y+z) = 0

 
(1)

                      x^3 \; + \; y^3 \; + \; z^3 \; = \; -(x + y + z)
 

316765^3 + (-254773)^3 + (-247968)^3 = -(316765-254773-247968) = 185976

181043234569^3 + (-145612450873)^3 + (-141723134784)^3
= -(181043234569-145612450873-141723134784)
= 106292351088

103473088198780357^3+(-83223048946797901)^3+(-81000157007929824)^3
= -(103473088198780357-83223048946797901-81000157007929824)
= 60750117755947368

59138801882773484444497^3+(-47565134948809366290865)^3+(-46294667735856472614528)^3
= -(59138801882773484444497-47565134948809366290865-46294667735856472614528)
= 34721000801892354460896

33800072550373118664240146029^3+(-27185282098289384542201602469)^3+(-26459161808334936488154174240)^3
= -(33800072550373118664240146029-27185282098289384542201602469-26459161808334936488154174240)
= 19844371356251202366115630680

 
(2)

                      x^3 \; + \; y^3 \; + \; z^3 \; = \; (x + y + z)
 

419^3 + (-337)^3 + (-328)^3 = (419-337-328) = -246

239474759^3 + (-192608725)^3 + (-187464136)^3
= \; (239474759-192608725-187464136) = -140598102

136868924808923^3 + (-110083205468713)^3 + (-107142877360840)^3
= \; (136868924808923-110083205468713-107142877360840)
= \; -80357158020630

78225791547202758815^3 + (-62916735086984681869)^3 + (-61236225840872307784)^3
= \; (78225791547202758815-62916735086984681869-61236225840872307784)
= \; -45927169380654230838

44709012449168301442798547^3+(-35959304938034967900575809)^3+(-34998830044533334168890952)^3
= \; (44709012449168301442798547-35959304938034967900575809-34998830044533334168890952)
= \; -26249122533400000626668214

 
 
 
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
This entry was posted in Number Puzzles and tagged . Bookmark the permalink.

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