Fourth Powers which are Sum of 4 Fourth Powers/Examples/651
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Examples of Fourth Powers which are Sum of 4 Fourth Powers
- $651^4 = 240^4 + 340^4 + 430^4 + 599^4$
Proof
| \(\ds 240^4 + 340^4 + 430^4 + 599^4\) | \(=\) | \(\ds 3 \, 317 \, 760 \, 000\) | ||||||||||||
| \(\ds \) | \(\) | \(\, \ds + \, \) | \(\ds 13 \, 363 \, 360 \, 000\) | |||||||||||
| \(\ds \) | \(\) | \(\, \ds + \, \) | \(\ds 34 \, 188 \, 010 \, 000\) | |||||||||||
| \(\ds \) | \(\) | \(\, \ds + \, \) | \(\ds 128 \, 738 \, 157 \, 601\) | |||||||||||
| \(\ds \) | \(=\) | \(\ds 179 \, 607 \, 287 \, 601\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 651^4\) |
$\blacksquare$
Sources
- Piezas, Tito III and Weisstein, Eric W. "Diophantine Equation--4th Powers." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/DiophantineEquation4thPowers.html