Smallest Number not Expressible as Sum of Fewer than 19 Fourth Powers

Theorem
The smallest positive integer which cannot be expressed as the sum of fewer than $19$ fourth powers is $79$:
 * $79 = 15 \times 1^4 + 4 \times 2^4$

Also see

 * Hilbert-Waring Theorem


 * 159 is not Expressible as Sum of Fewer than 19 Fourth Powers
 * 319 is not Expressible as Sum of Fewer than 19 Fourth Powers