On the equation  <IMG WIDTH="124" HEIGHT="43" ALIGN="MIDDLE" BORDER="0" SRC="/mcom/2008-77-262/S0025-5718-07-02083-2/gif-title0/img1.gif" ALT="$ s^2+y^{2p} = \alpha^3$">期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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On the equation $s^2+y^{2p} = \alpha^3$

Authors:	Imin Chen

Institution:	Department of Mathematics, Simon Fraser University, Burnaby, B.C., Canada V5A 1S6

Abstract:	We describe a criterion for showing that the equation $s^2+y^{2p} = \alpha^3$ has no non-trivial proper integer solutions for specific primes . This equation is a special case of the generalized Fermat equation . The criterion is based on the method of Galois representations and modular forms together with an idea of Kraus for eliminating modular forms for specific in the final stage of the method (1998). The criterion can be computationally verified for primes and $p \not= 31$ .

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