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Jeremy Rouse
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To see that $f_{1}$, $f_{2}$, $\ldots$, $f_{k}$ must be scalar multiples of $f_{k+1}$, plug in the root of $f_{k+1}$ into both sides of the equation.

Jeremy Rouse
  • 20.4k
  • 2
  • 79
  • 105