VARIANTS OF ERDŐS–SELFRIDGE SUPERELLIPTIC CURVES AND THEIR RATIONAL POINTS

For the superelliptic curves of the form $$\begin{eqnarray}(x+1)\cdots (x+i-1)(x+i+1)\cdots (x+k)=y^{\ell }\end{eqnarray}$$ with $y\neq 0$ , $k\geqslant 3$ , $\ell \geqslant 2,$ a prime and for $i\in [2,k]\setminus \unicode[STIX]{x1D6FA}$ , we show that $\ell

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Veröffentlicht in:	Mathematika 2018, Vol.64 (2), p.380-386
Hauptverfasser:	Das, Pranabesh, Laishram, Shanta, Saradha, N.
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Sprache:	eng
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creator	Das, Pranabesh Laishram, Shanta Saradha, N.
description	For the superelliptic curves of the form $$\begin{eqnarray}(x+1)\cdots (x+i-1)(x+i+1)\cdots (x+k)=y^{\ell }\end{eqnarray}$$ with $y\neq 0$ , $k\geqslant 3$ , $\ell \geqslant 2,$ a prime and for $i\in [2,k]\setminus \unicode[STIX]{x1D6FA}$ , we show that $\ell
doi_str_mv	10.1112/S0025579317000559
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title	VARIANTS OF ERDŐS–SELFRIDGE SUPERELLIPTIC CURVES AND THEIR RATIONAL POINTS
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