IRREDUCIBILITY OF POLYNOMIALS AND DIOPHANTINE EQUATIONS

@inproceedings{Woo2010IRREDUCIBILITYOP,
  title={IRREDUCIBILITY OF POLYNOMIALS AND DIOPHANTINE EQUATIONS},
  author={Sung Sik Woo},
  year={2010}
}
In (3) we showed that a polynomial over a Noetherian ring is divisible by some other polynomial by looking at the matrix formed by the coecients of the polynomials which we called the resultant matrix. In this paper, we consider the polynomials with coecients in a field and divisibility of a polynomial by a polynomial with a certain degree is equivalent to the existence of common solution to a system of Diophantine equations. As an application we construct a family of irreducible quartics over… CONTINUE READING

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