How is it possible for a polynomial to factor (poly mod n) but have no roots? That is no integers x such that . Give an example of a polynomial that factors (poly mod n) and prove that it has no roots. I'm completely stumped.
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Hello, Originally Posted by Pn0yS0ld13r How is it possible for a polynomial to factor (poly mod n) but have no roots? That is no integers x such that . Give an example of a polynomial that factors (poly mod n) and prove that it has no roots. I'm completely stumped. Here are some examples : If n=2, in , has no root. (and it's the only one if n=2) So you can take as an example : this factors into but it has no root . Check it out : doesn't give any zero for
Last edited by Moo; Jul 29th 2008 at 02:29 PM. Reason: simplified a little more
Let's see for . has no root (once again, check it out ) also has no root . Thus can be factored, but has no root
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