A note on diophantine equation 𝑌²+𝑘=𝑋⁵

Blass, Josef

doi:10.1090/S0025-5718-1976-0401638-2

A note on diophantine equation $Y^{2}+k=X^{5}$
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by Josef Blass PDF

Math. Comp. 30 (1976), 638-640 Request permission

Abstract:

We show that if the class number of the quadratic field $A(\sqrt { - k} )$ is not divisible by 5, and if k is not congruent to 7 modulo 8, then the equation ${Y^2} + k = {X^5}$ has no solutions in rational integers X, Y with the exception of $k = 1,19,341$.

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Amer. Math. Monthly,

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