Talk:Casas-Alvero conjecture

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Confused by Difficulty

If f is a polynomial of degree d, then f^(d-1)(x) is a linear function such that f^(d-1)(a) = 0.

Thus, f^(d-1)(x) = c_d-1*(x - a), where c_n is a constant.

f^(d-2)(x) = c_d-1*(x - a)²/2 = c_d-2*(x - a)²,

and continued integration gives f(x) = c₀*(x - a)^d.

Since it has characteristic zero, a constant cannot be added to each integration since that would negate f^(d-1)(a) = 0.

Note: The only caveat to the conjecture, which it does not explicitly say, is that the function has to be a constant times the power of a linear function.

Am I missing something? BAbdulBaki (talk) 21:39, 3 November 2024 (UTC)

The conjecture only says some factor is shared, not that that factor must be a constant. The point is to prove that is must be a constant factor. David Malone (talk) 22:34, 3 November 2024 (UTC)

Thank you! Now it makes sense. Not sure why I didn't read it as that. BAbdulBaki (talk) 00:44, 4 November 2024 (UTC)