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MathNet 2009-part-01 — 175 problems (EN–VI) Question 15

Math Olympiad Vault · MathNet 2009-part-01 — 175 problems (EN–VI)

Question 15

Find all perfect powers that end with the digits 2, 0, 0, 8, in that order.

CLARIFICATION: A perfect power is a number of the form $a^k$ where $a$ and $k$ are positive integers and $k \geq 2$. For example, $6^2$; $2^7$; $100^3$.