Sophie Germain's theorem for prime pairs \(p, 6p+1\)
type: Item
instance of: scholarly article
title: Sophie Germain's theorem for prime pairs \(p, 6p+1\)
zbMATH Open document ID: 0622.10013
DOI: 10.1016/0022-314X(87)90052-7
author: Andrew Granville
published in: Journal of Number Theory
publication date: 1987-01-01T00:00:00Z
review text: Let \(p\) be an odd prime and suppose that there exist integers \(X, Y, Z\) prime to \(p\) satisfying the Fermat equation \(X^p+Y^p+Z^p=0\). Suppose that \(q=6p+1\) is a prime. Working in the quadratic field \(\mathbb Q(\sqrt{-3})\), the author deduces from this certain rational divisibility conditions depending on \(q\). His computations show that among the \(14443\) prime pairs \((p,q)\) with \(p<10^6\) there are \(1615\) pairs satisfying these conditions.
Mathematics Subject Classification ID: 11D41
zbMATH DE Number: 4008481
zbMATH Keywords: first case of Fermat's last theorem
zbMATH Keywords: rational divisibility conditions
zbMATH Keywords: prime pairs
MaRDI profile type: Publication
cites work: Q3904661
cites work: Q4149520
full work available at URL: 0022-314x(87)90052-7
OpenAlex ID: W2048402303
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description: scientific article; zbMATH DE number 4008481