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25563Problem solution equation: x^k.f(x)+y^k.f(y)=z^k*f(z)

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  • yeuemtrondoitb85
    Jun 24, 2014
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      Dear all Member,

      Let a polynomial function: 

       f(x) =  x^n + a_{n-1} x^{n-1} +.... + a_2 x^2 + a_1 x + a_0 . Where $n$ is positive integer, $n \geq 3$ and $a_0, a_1, a_2, ..., a_n $ are constant coefficients $\in Z$ and has no integer x can satisfy the equation:  $f(x)=0$. 

      Find all positive integer x,y,z can satisfy equation:

      x^k.f(x)+y^k.f(y)=z^k*f(z)  where: k is a positive interger and k+n \geq 3

      Best regards


      Dao Thanh Oai