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10 naturals of arithmetic progression. wanted

Source: Argentina 1997 OMA L3 p6

May 13, 2024
arithmetic sequencenumber theory

Problem Statement

Decide if there are ten natural and distinct numbers a1,a2,…,a10a_1,a_2,\ldots ,a_{10} such that: ∙\bullet Each of them is a power of a natural number with a natural exponent and greater than 11. ∙\bullet The numbers a1,a2,…,a10a_1,a_2,\ldots ,a_{10} form an arithmetic progression.
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