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On Fixed Divisors of Forms in Many Variables, I

A. Schinzel

Abstract


Let $D_{d,r}$ be the maximal fixed divisor of a primitive form of degree $d$ in $r$ variables over $\mathsf{Z}$. A formula is given for $D_{d,2}$ and estimates for $D_{d,r}$ for $r>2$. As a consequence, a question of Nagell raised in 1919 is completely answered.

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DOI: http://dx.doi.org/10.7146/math.scand.a-17104

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ISSN 0025-5521 (print) ISSN 1903-1807 (online)

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