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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 - Primes represented by polynomials; other multiplicative structure of polynomial values 11D41 - Higher degree equations; Fermat's equation