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## Main Question or Discussion Point

Does anyone know if this is true and if so where they know it from?

Given a polynomial over the integers there exists a finite field K of prime order p, such that p does not divide the first or last coefficient, and the polynomial splits over K.

I realize this could be considered an abstract algebra question but I feel that this could easily have an elementary number theory proof. Of course I would love to see a reference in an algebra text of this result as well.

Thanks a lot,

Steven

Given a polynomial over the integers there exists a finite field K of prime order p, such that p does not divide the first or last coefficient, and the polynomial splits over K.

I realize this could be considered an abstract algebra question but I feel that this could easily have an elementary number theory proof. Of course I would love to see a reference in an algebra text of this result as well.

Thanks a lot,

Steven