Symmetric polynomial

Number Theory Level 2

True or False?

The only triplet of non-negative integers ( x , y , z ) (x,y,z) satisfying x 3 + y 3 + z 3 = 2 x y z x^3 + y^3 + z^3 = 2xyz is ( x , y , z ) = ( 0 , 0 , 0 ) (x,y,z) = (0,0,0) .

False True

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Prayas Rautray by Prayas Rautray , 20, India

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1 solution

Md Junaid
Oct 7, 2017

I guess it can be proved that x=y=z=0 is the only solution by Fermat's Law Of Infinite Descent. :P

I guess :P Not sure

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