Fourth Powers which are Sum of 4 Fourth Powers/Examples/353

Examples of Fourth Powers which are Sum of 4 Fourth Powers

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

Proof
Now we have that:

Hence:

But:
 * $3 \times 17 = 2 \times 26 - 1$

So:

Hence:
 * $353^2 + 272^2 = 2^4 + 8^4 + 21^4$

but:

So:
 * $353^4 = 30^4 + 120^4 + 272^4 + 315^4$