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Since the Japanese occupation of Korea plays such a big part in the histories of both North and South Korea, what would need to happen for Korea to not become a Japnese protectorate in 1905 and then outright annexed by Japan in 1910?
(Disclaimer: I am fully aware that the aforementioned events happened after 1900, but since the groundwork happened in the 19th Century, that's why I'm putting it in the Before 1900 forum).