Luis H. Gallardo, Joshua Zelinsky
In this note, we fix a gap in a proof of the first author that 28 is the only even perfect number which is the sum of two perfect cubes. We also discuss the situation for higher powers.
This paper contains 1 section, 1 theorem, 49 equations.
Proposition 3
Assume that Conjecture 2 holds. Assume that $2^p-1$ is prime. Then there is no simultaneous solution in positive integers satisfying the following list of conditions: (a) $m > 29$, (b) $(x+a)^{m-2} \leq x^m+a^m$, (c) Both $x$ and $a$ are odd, (d) $x+a = 2^h$, (e) $\frac{x^m+a^m}{x+a} = (2^p-1) \cdot
