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positive integer a

Source: Ukraine 1997 grade 9

July 18, 2009
number theory unsolvednumber theory

Problem Statement

Does there exist a positvie integer a a such that all the numbers a,2a,3a,...,1997a a,2a,3a,...,1997a are perfect powers (i.e. numbers of the form mk m^k, where m,k∈N m,k \in \mathbb{N}, k≥2 k \ge 2)?
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