Assume that f + f + f for n > 3 and three non constant polynomial...

 

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Assume that f + f + f for n > 3 and three non constant polynomial f₁ f₁.f3 € C[X] without a common factor. Set α = ²mi/n € C. Iff and f have a common irreducible factor, than it is alos a divisor for fi and thus the whole equation. Son ow we can assume that fand f have no common irreducible factor. We can also assume that deg f¹ + deg f² + deg f³ > 0 is as small as possible. Also assume that f₁ =¹f3-a¹f₂) and f₁-f₂ = g², f3-af₂ = g², f₂ -α²f₂ = g² Question: Proof that for a well chosen a, b = C, (ag₁)" + (bg₂)" = g Assume that f + f + f for n > 3 and three non constant polynomial f₁ f₁.f3 € C[X] without a common factor. Set α = ²mi/n € C. Iff and f have a common irreducible factor, than it is alos a divisor for fi and thus the whole equation. Son ow we can assume that fand f have no common irreducible factor. We can also assume that deg f¹ + deg f² + deg f³ > 0 is as small as possible. Also assume that f₁ =¹f3-a¹f₂) and f₁-f₂ = g², f3-af₂ = g², f₂ -α²f₂ = g² Question: Proof that for a well chosen a, b = C, (ag₁)" + (bg₂)" = g

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