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Originally Posted by wblipp
Does the root need to be small, too?
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A bit more musing shows me the root can probably be large. It not, then the highest possible value for the polynomial is about 10
72. so the only way to make the modular value zero would be to make the polynomial value zero, which would mean that (x-r) is a factor of the polynomial. Since it's trivial to create such polynomials as (x-r) times anything, it's unlikely such polynomials are of any use.