MathDB

6

Part of 1997 Argentina National Olympiad

Problems(1)

10 naturals of arithmetic progression. wanted

Source: Argentina 1997 OMA L3 p6

5/13/2024
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.
arithmetic sequencenumber theory