Fourth Power expressible as Sum of 6 Fourth Powers
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Theorem
$28 \, 561$ can be expressed as the sum of $6$ fourth powers:
- $28 \, 561 = 13^4 = 12^4 + 8^4 + 7^4 + 6^4 + 2^4 + 2^4$
Proof
| \(\ds \) | \(\) | \(\ds 12^4 + 8^4 + 7^4 + 6^4 + 2^4 + 2^4\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 20 \, 736 + 4096 + 2401 + 1296 + 16 + 16\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 28 \, 561\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 13^4\) |
$\blacksquare$
Sources
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $28,561$