# Fourth Powers which are Sum of 4 Fourth Powers

## Theorem

The following positive integers are such that their fourth powers can be expressed as the sum of the fourth powers of $4$ other positive integers with no common factors:

$353, 651, 2487, 2501, 2829, \ldots$

## Examples

### 353

$353^4 = 30^4 + 120^4 + 272^4 + 315^4$

### 651

$651^4 = 240^4 + 340^4 + 430^4 + 599^4$