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

\(\displaystyle 240^4 + 340^4 + 430^4 + 599^4\) \(=\) \(\displaystyle 3 \, 317 \, 760 \, 000\)
\(\displaystyle \) \(\) \(\, \displaystyle + \, \) \(\displaystyle 13 \, 363 \, 360 \, 000\)
\(\displaystyle \) \(\) \(\, \displaystyle + \, \) \(\displaystyle 34 \, 188 \, 010 \, 000\)
\(\displaystyle \) \(\) \(\, \displaystyle + \, \) \(\displaystyle 128 \, 738 \, 157 \, 601\)
\(\displaystyle \) \(=\) \(\displaystyle 179 \, 607 \, 287 \, 601\)
\(\displaystyle \) \(=\) \(\displaystyle 651^4\)

$\blacksquare$


Sources