H. Ancient Wisdom

Codeforces

IDCF10236H

Time1000ms

Memory1024MB

Difficulty—

English · Original

Formal · Original

David and Aram had the following conversation: David: "_Aram, you're pretty old._" Aram: "_I'm not THAT old. If you cube your age and then multiply by $C$, you'd get exactly my age squared._" Lucca overheard this conversation but isn't sure if he caught the right value for $C$. Help Lucca figure out how young David could be, assuming he heard correctly. As everyone knows, ages are positive integers. Input is a single integer, what Lucca thought he heard for the value of $C$ $(1 <= C < 2^(63))$. Output the minimum age David could be. The average computer can do roughly $10^8$ elementary operations in one second. If you submit a program that tries to do more than $10^9$ operations, you shouldn't be surprised if your program gets a Time Limit Exceeded verdict! ## Input Input is a single integer, what Lucca thought he heard for the value of $C$ $(1 <= C < 2^(63))$. ## Output Output the minimum age David could be. [samples] ## Note The average computer can do roughly $10^8$ elementary operations in one second. If you submit a program that tries to do more than $10^9$ operations, you shouldn't be surprised if your program gets a Time Limit Exceeded verdict!

Let $ C \in \mathbb{Z}^+ $ with $ 1 \leq C < 2^{63} $. Find the minimum positive integer $ d $ such that there exists a positive integer $ a $ satisfying: $$ C \cdot d^3 = a^2 $$

API Response (JSON)

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