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## Main Question or Discussion Point

Fermat's last theorem states that the diophantine equation

[tex] x^n + y^n = z^n [/tex]

does not have solutions if [tex] xyz \neq 0 [/tex] and n > 2. Now and Indian mathematician, Dhananjay P. Mehendal have conjectured a generalization of FLT. His (or her, I'm no good at Indian names) states that the diophantine equation

[tex] \sum_{i=1}^{n} x_i^k = z^k [/tex]

with 1 < n < k does not have a solution if [tex] \prod_{i=1}^{n} x_i \neq 0 [/tex]. This conjecture is true for n=2, becaue this case is Fermat's last theorem which Wiles proved in the mid 90ies. However do you think the conjecture is true for all n, or can you easily find a counter-exampel to the suggested conjecture?

[tex] x^n + y^n = z^n [/tex]

does not have solutions if [tex] xyz \neq 0 [/tex] and n > 2. Now and Indian mathematician, Dhananjay P. Mehendal have conjectured a generalization of FLT. His (or her, I'm no good at Indian names) states that the diophantine equation

[tex] \sum_{i=1}^{n} x_i^k = z^k [/tex]

with 1 < n < k does not have a solution if [tex] \prod_{i=1}^{n} x_i \neq 0 [/tex]. This conjecture is true for n=2, becaue this case is Fermat's last theorem which Wiles proved in the mid 90ies. However do you think the conjecture is true for all n, or can you easily find a counter-exampel to the suggested conjecture?