K. Mahler, An unsolved problem on the powers of , J. Austral. Math. Soc., 8 (1968) 313--321. The problem Mahler studies was originally proposed by Prof. Saburô Uchiyama (Tsukuba Univ.), according to S. Ando [2]. It arose indirectly in connection with the function of Waring's problem, see G. H. Harding and E. M. Wright, An Introduction to the Theory of Numbers (4th ed.), Oxford Univ. Press, 1960, Theorem 393ff.
[1] [2]