Chowla, S.
(1970)
*An idea of tate-dwork for the "hasse invariant" applied to a classical theorem of Fermat*
Journal of Number Theory, 2
(4).
pp. 423-424.
ISSN 0022-314X

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Official URL: http://linkinghub.elsevier.com/retrieve/pii/002231...

Related URL: http://dx.doi.org/10.1016/0022-314X(70)90045-4

## Abstract

Let p denote a prime ≡ 1 (mod 4). We have (Fermat) p = a^{2} + b^{2} where (say) a ≡ 1 (mod 4). It is proved that α ≡±(1/2)F_{(p + 1)/2} ( 1/2, 1/2, 1; -1) where F_{n}(α, β, γ; x) stands for the sum of the first n terms of the hypergeometric series F(α, β, γ; x). The sign is + or − according as p≡ 1 (mod 8) or p ≡ 5 (mod 8).

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ID Code: | 8771 |

Deposited On: | 28 Oct 2010 11:12 |

Last Modified: | 05 Dec 2011 03:54 |

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