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?
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Are 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. – Michael Rozenberg Feb 11 '17 at 15:36
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There must be. It has been my challenge trying to figure it out. – Feb 11 '17 at 15:40
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This function is examined in detail in Ribenboim’s Fermat’s Last Theorem for Amateurs, Chapter VII.
Kieren MacMillan
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