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In 1958, Sierpinski asked whether there exists a linear order $X$ that isisomorphic to its lexicographically ordered cube but is not isomorphic to itssquare. The main result of this paper is that the answer is negative. Moregenerally, if $X$ is isomorphic to any one of its finite powers $X^n$, $n>1$,it is isomorphic to all of them.

Every linear order isomorphic to its cube is isomorphic to its square