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Gene Ward Smith wrote:
>
> I've had fun with some issues raised in recent threads. I think asking
> what it means to claim divisibility is distributed unevenly among the
> roots of an irreducible monic polynomial is an interesting topic.
Over the years his rubbish has generated several interesting spin offs,
well at least one that comes to mind:
Show that a polynomial sum(a_i.x^i) with rational integer coefficients
a_i can be expressed as a product of linear factors b_i.x + c_i with
every b_i, c_i an algebraic integer.
Looks trivial at first sight; but if the leading coefficient is not
+/-1
(and assuming the coefficients are relatively prime) it certainly
isn't,
even for a quadratic.
I think Arturo Magidin (and a colleague?) ended up writing a paper
on the problem.
Cheers
John R Ramsden
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