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# Generalizing Fermat's Last Theorem

## Question

Have there been any developments since the proof of FLT? Are there any generalizations to FLT that are actively being studied these days? In particular, given n, what is the least number m such that z^n = x_1^n + x_2^n + … + x_m^n has integral solutions? On the other hand, given m, what is the least number n such that z^n = x_1^n + x_2^n + … + x_m^n has integral solutions? It would be nice if someone with such knowledge can put in a word or two about it in the Encyclopedia.

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## Homogenenous diophantine equations

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