Fourth Powers which are Sum of 4 Fourth Powers/Mistake

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Source Work

1997: David Wells: Curious and Interesting Numbers (2nd ed.):

The Dictionary
$353$


Mistake

$353^4$ is the smallest number that is the sum of $4$ other $4$th powers ... The sequence of such numbers continues: $651 \quad 2487 \quad 2501 \quad 2829 \ldots$


It needs to be specified that the $4$th powers themselves must have no common divisor, otherwise, for example, $706$ would be included in this list:

\(\ds 60^4 + 240^4 + 544^4 + 630^4\) \(=\) \(\ds 12 \, 960 \, 000\)
\(\ds \) \(\) \(\, \ds + \, \) \(\ds 3 \, 317 \, 760 \, 000\)
\(\ds \) \(\) \(\, \ds + \, \) \(\ds 87 \, 578 \, 116 \, 096\)
\(\ds \) \(\) \(\, \ds + \, \) \(\ds 157 \, 529 \, 610 \, 000\)
\(\ds \) \(=\) \(\ds 248 \, 438 \, 446 \, 096\)
\(\ds \) \(=\) \(\ds 706^4\)


Sources