Y by Smita, Adventure10, Mango247
Find all polynomials
with real coefficents, such that for all
satisfying
, the equation below is true: ![\[P(x+y)^3+P(y+z)^3+P(z+x)^3=3P((x+y)(y+z)(z+x))\]](//latex.artofproblemsolving.com/5/1/7/517cf8a90af0a7f1d15c47fc95a704ebf55f3ebd.png)



![\[P(x+y)^3+P(y+z)^3+P(z+x)^3=3P((x+y)(y+z)(z+x))\]](http://latex.artofproblemsolving.com/5/1/7/517cf8a90af0a7f1d15c47fc95a704ebf55f3ebd.png)
This post has been edited 2 times. Last edited by IstekOlympiadTeam, May 26, 2018, 11:03 AM
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