559 is not Expressible as Sum of Fewer than 19 Fourth Powers

Theorem
$559$ cannot be expressed as the sum of fewer than $19$ fourth powers:
 * $559 = 15 \times 1^4 + 2 \times 2^4 + 2 \times 4^4$

or:
 * $559 = 9 \times 1^4 + 4 \times 2^4 + 6 \times 3^4$

Also see

 * Hilbert-Waring Theorem


 * Numbers not Expressible as Sum of Fewer than 19 Fourth Powers