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The Number of Fields Generated by the Square Root of Values of a Given Polynomial

  Published:2003-03-01
 Printed: Mar 2003
  • Pamela Cutter
  • Andrew Granville
  • Thomas J. Tucker
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Abstract

The $abc$-conjecture is applied to various questions involving the number of distinct fields $\mathbb{Q} \bigl( \sqrt{f(n)} \bigr)$, as we vary over integers $n$.
MSC Classifications: 11N32, 11D41 show english descriptions Primes represented by polynomials; other multiplicative structure of polynomial values
Higher degree equations; Fermat's equation
11N32 - Primes represented by polynomials; other multiplicative structure of polynomial values
11D41 - Higher degree equations; Fermat's equation
 

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