IrMO 1998 P1 Q3: Cubes and Bases: Upper Secondary Mathematics Competition Question

Show that no integer of the form xyxy in base 10, where x and y are digits, can be the cube of an integer.

Find the smallest base b > 1 for which there is a perfect cube of the form xyxy in base b.


[Irish MO (IrMO) 1998 Paper 1 Question 3]

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