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min pos. integer x such that 2x=a^2, 2x=b^3, 5x=c^2

Source: Austria Beginners' Competition 2011 p1

October 3, 2021
Perfect PowersPerfect powernumber theory

Problem Statement

Let xx be the smallest positive integer for which 2x2x is the square of an integer, 3x3x is the third power of an integer, and 5x5x is the fifth power of an integer. Find the prime factorization of xx.
(St. Wagner, Stellenbosch University)
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