If $R$ is a ring such that $x^5=x$ for all $x\in R$, is $R$ commutative?
If the answer to the above question is yes, then what is the least positive integer $k \ge 6$, such that there exists a noncommutative ring $R$ with $x^k=x$ for all $x\in R$?
If $R$ is a ring such that $x^5=x$ for all $x\in R$, is $R$ commutative?
If the answer to the above question is yes, then what is the least positive integer $k \ge 6$, such that there exists a noncommutative ring $R$ with $x^k=x$ for all $x\in R$?