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
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $353$