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Unsolved Challenge Evaluate Algebraic Expression

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anemone

MHB POTW Director
Staff member
Feb 14, 2012
3,802
Let $a,\,b,,c \in \mathbb R$ such that $ab+bc+ca=0$ and $abc\ne 0$. Evaluate $\dfrac{a^5+b^5+c^5-1}{abc}$.