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

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## Contents

## Theorem

$319$ cannot be expressed as the sum of fewer than $19$ fourth powers:

- $319 = 15 \times 1^4 + 3 \times 2^4 + 4^4$

or:

- $319 = 12 \times 1^4 + 4 \times 2^4 + 3 \times 3^4$

## Proof

## Also see

- Smallest Number not Expressible as Sum of Fewer than 19 Fourth Powers
- 159 is not Expressible as Sum of Fewer than 19 Fourth Powers
- 399 is not Expressible as Sum of Fewer than 19 Fourth Powers

## Sources

- 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): $319$ - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $319$