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We know that x1^n + x2^n = y^n has no solution for n > 2. However, what about this?

For which values of k does x1^n+x2^n+...+xk^n = z^n have solutions for n > k?

We know it's true for 1 ((-1)^2 = 1^2) and not true for 2. What about other numbers?

Thanks in advance,

ACG