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gmvh
gmvh
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Example:
for $n = 2$, $k = 2$, the set $\{ x | -2^2+1\leq x\leq 2^2\}$ can be splitedsplit into {-1, 1, 2, 4} and {-3, -2, 0, 3}, as $(-1)^2+1^2+2^2+4^2=(-3)^2+(-2)^2+0^2+3^2$

I wonder if this problem has its own name and some relative researchsrelated research. I would appreciate it if anyone could give some useful information. Thanks a lot.

Example:
for $n = 2$, $k = 2$, the set $\{ x | -2^2+1\leq x\leq 2^2\}$ can be splited into {-1, 1, 2, 4} and {-3, -2, 0, 3}, as $(-1)^2+1^2+2^2+4^2=(-3)^2+(-2)^2+0^2+3^2$

I wonder if this problem has its own name and some relative researchs. I would appreciate it if anyone could give some useful information. Thanks a lot.

Example:
for $n = 2$, $k = 2$, the set $\{ x | -2^2+1\leq x\leq 2^2\}$ can be split into {-1, 1, 2, 4} and {-3, -2, 0, 3}, as $(-1)^2+1^2+2^2+4^2=(-3)^2+(-2)^2+0^2+3^2$

I wonder if this problem has its own name and some related research. I would appreciate it if anyone could give some useful information. Thanks a lot.

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Solarius
Solarius
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Given integer n and k, split the set {x| - 2^n + 1 ≤ x ≤ 2^n} into two subsets A and B, so that |A| = |B| and $\sum_{a\in A}a^k=\sum_{b\in B}b^k$

Example:
for $n = 2$, $k = 2$, the set $\{ x | -2^2+1\leq x\leq 2^2\}$ can be splited into {-1, 1, 2, 4} and {-3, -2, 0, 3}, as $(-1)^2+1^2+2^2+4^2=(-3)^2+(-2)^2+0^2+3^2$

I wonder if this problem has its own name and some relative researchs. I would appreciate it if anyone could give some useful information. Thanks a lot.