Let $x,y,z$ be integers where $(x+y)(y+z) (z+x)\neq 0$ and $ n$ is odd prime. Find the summation notation of: $$f(x,y,z)=\dfrac{(x+y+z)^n-(x^n+y^n+z^n)}{ (x+y)(y+z) (z+x)}$$ Any hints?
What is the summation notation of: $f(x,y,z)=\dfrac{(x+y+z)^n-(x^n+y^n+z^n)}{ (x+y)(y+z) (z+x)}$?
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diophantine-equations
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0Are you sure that there is something? For $n=3$, $n=5$, $n=7$, $n=9$ we can get these sums easily, but from $n=11$ it takes time. – 2017-02-11
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0There must be. It has been my challenge trying to figure it out. – 2017-02-11
1 Answers
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This function is examined in detail in Ribenboim’s Fermat’s Last Theorem for Amateurs, Chapter VII.