What is the authenticity of the Hadith: "I am innocent of whoever lives forty days amongst the polytheists," and what is the Shar'i ruling on a Muslim residing in the lands of disbelief for work or study?

The correct wording of the hadith is: "I am free of any Muslim who resides among the polytheists." They said, "Why, O Messenger of Allah?" He said, "Their fires should not be visible to each other." The ruling on residing in a land of polytheism for the purpose of work or study varies depending on the condition of the resident. If he is secure in his religion, able to perform his rituals, and possesses knowledge and piety that repel doubts and temptations, then it is permissible for him to stay. As for one who is not secure in his religion, it is not permissible for him to stay, and he must emigrate if he fears apostasy (fitna) in his religion and cannot practice it openly.