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Modular elliptic curves over real abelian fields and the generalized Fermat equation x2โ„“+ y2m= zp

Modular elliptic curves over real abelian fields and the generalized Fermat equation x2โ„“+ y2m= zp

Let K be a real abelian field of odd class number in which 5 is unramified.Let S 5 be the set of places of K above 5.Suppose for every nonempty proper subset S โŠ‚ S 5 there is a totally positive unit u โˆˆ O K such that qโˆˆS Norm โ€ฆ