Equal Sums of Like Powers

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- May 26th 2010, 04:38 PMwonderboy1953Equal Sums of Like Powers
- May 27th 2010, 08:45 AMhollywood
Interesting.

It seems to be a little old - May 6, 2001. Also, it seems to be focused on small solutions - large solutions can be useful, too.

Someone on MHF has an example of equal sums of like powers in their signature, but I forgot who. I looked around and found Swlabr has $\displaystyle 3987^{12}+4365^{12}=4472^{12}$, but that's not the one I was thinking of. By the way, is Swlabr's counter-example to FLT some kind of inside joke?

- Hollywood - May 27th 2010, 10:44 AMundefined
- May 27th 2010, 04:21 PMhollywood
Yes, that's it.

The site in question seems to be looking only for cases with the same number of terms on both sides. Of course, I suppose you can set some of the numbers to zero. Also, they are looking for cases where the equation is true for multiple exponents. Here's an interesting example from the site:

$\displaystyle 975^2+224368^2+300495^2+366448^2=37648^2+202575^2+ 337168^2+344655^2$

$\displaystyle 975^3+224368^3+300495^3+366448^3=37648^3+202575^3+ 337168^3+344655^3$

$\displaystyle 975^4+224368^4+300495^4+366448^4=37648^4+202575^4+ 337168^4+344655^4$

- Hollywood - May 28th 2010, 07:32 AMwonderboy1953Hollywood
- May 29th 2010, 02:55 AMroninpro
I think that this "counter-example" may have appeared in a Simpsons episode.

Fermat's Last Theorem in fiction - Wikipedia, the free encyclopedia