I moved from California to Hong Kong, Residency wasn't a problem as i had lived here before and registered my own company and invested money in property etc which seemed to speed up the whole process.
Different countries have different requirements for visa/residency. Some countries require sponsorship to gain a work visa, while others will give you residency if you are willing to invest x amount of money into the country.
Also remember that just because you leave the US doesnt mean you dont have to pay US taxes...if you make over a certain amount per year the income is taxable.
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