Burnside problem

Statement
For what values of $$n$$ are the following equivalent conditions true?


 * 1) Every group of exponent $$n$$ is locally finite
 * 2) Every finitely generated group of exponent $$n$$ is finite
 * 3) For every positive integer $$n$$, the Burnside group $$B(d,n)$$ is a finite group.

Note that, at least prima facie, it is possible, for a given $$n$$, that $$B(d,n)$$ is finite for small $$d$$ but infinite for large $$d$$.