A computation in Bremner is incorrect. Examples 12, 13 state that the Diophantine equations x4 + y4 = D,, with D = 4481, 5617, can have no solution in any cubic number field. The presented argument reduced the problem to a system of three simultaneous quartic equations in four variables, which were asserted to have no solution in an appropriate p-adic field (p = 17, 41, respectively). This latter computation is not correct, as can be seen by the following. Example: Let K = Q(θ) be the cubic number field defined by θ3 − θ2 + 10θ + 24 = 0. Then (Formula presented.) Example: Let (Formula presented.) be the cubic number field defined by φ3 − 7φ − 256 = 0. Then (Formula presented.) This observation regarding the examples does not affect the remaining results of the paper.
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