Jha, Vijay On Krasnér’s theorem for the first case of Fermat’s last theorem. (English) Zbl 0813.11015 Colloq. Math. 67, No. 1, 25-31 (1994). The solvability of the Fermat equation \(x^ p + y^ p = z^ p\) \((p\) an odd prime) in the so-called first case would imply that \(p\) divides the Bernoulli numbers \(B_{p-n-1}\) for all \(n\) up to \(k(p) = 2[(\log p)^{1/3}]\). This is the content of M. Krasner’s classical theorem supplemented by a computational result. The author studies various ways of increasing the bound \(k(p)\). By modifying an argument in Krasner’s proof he achieves the bound \(\max \{(2(\log p)/ \log \log p)^{1/2}\), \((\log p)^{617/1398}\}\), which is slightly better than a bound obtained by A. Granville [Manuscr. Math. 56, 67-70 (1986; Zbl 0599.10013)]. Reviewer: T.Metsänkylä (Turku) MSC: 11D41 Higher degree equations; Fermat’s equation 11B68 Bernoulli and Euler numbers and polynomials Keywords:first case of Fermat’s last theorem; Fermat equation; Bernoulli numbers Citations:Zbl 0599.10013 PDFBibTeX XMLCite \textit{V. Jha}, Colloq. Math. 67, No. 1, 25--31 (1994; Zbl 0813.11015) Full Text: DOI EuDML