On the Equation
نویسنده
چکیده
We describe a criterion for showing that the equation s2+y2p = α3 has no non-trivial proper integer solutions for specific primes p > 7. This equation is a special case of the generalized Fermat equation xp + yq + zr = 0. 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 p in the final stage of the method (1998). The criterion can be computationally verified for primes 7 < p < 107 and p = 31.
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