E. Mahmoud and Ehab and the xor-MST

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      "content": "Ehab is interested in the bitwise-xor operation and the special graphs. Mahmoud gave him a problem that combines both. He has a complete graph consisting of _n_ vertices numbered from 0 to _n_ - 1. Fo",
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      "content": "Ehab is interested in the bitwise-xor operation and the special graphs. Mahmoud gave him a problem that combines both. He has a complete graph consisting of _n_ vertices numbered from 0 to _n_ - 1. Fo...",
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      "content": "**Definitions**  \nLet $ n \\in \\mathbb{Z} $ with $ 2 \\leq n \\leq 10^{12} $.  \nConsider the complete graph $ G = (V, E) $ where:  \n- $ V = \\{0, 1, 2, \\dots, n-1\\} $,  \n- For every pair $ u, v \\in V $ wi...",
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