Fifth Power expressible as Sum of 4 Fifth Powers
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Theorem
$61 \, 917 \, 364 \, 224$ can be expressed as the sum of $4$ fifth powers:
- $61 \, 917 \, 364 \, 224 = 144^5 = 27^5 + 84^5 + 110^5 + 133^5$
Proof
| \(\ds \) | \(\) | \(\ds 27^5 + 84^5 + 110^5 + 133^5\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 14 \, 348 \, 907 + 4 \, 182 \, 119 \, 424 + 16 \, 105 \, 100 \, 000 + 41 \, 615 \, 795 \, 893\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 61 \, 917 \, 364 \, 224\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 144^5\) |
$\blacksquare$
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $61,917,364,224$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $61,917,364,224$