MHB Solving for $k$: Digit Product = $\dfrac{25k}{8}-211$

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The discussion focuses on finding positive integers \( k \) such that the product of the digits of \( k \) equals \( \frac{25k}{8} - 211 \). Participants confirm that both 72 and 88 satisfy this equation. There is a suggestion to share the solution with MHB for further insights. The conversation emphasizes the importance of verifying the conditions for \( k \) to ensure all solutions are identified. Overall, the thread highlights a mathematical exploration of digit products in relation to a linear equation.
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Find all positive integers $k$ such that the product of the digits of $k$, in the decimal system, equals $\dfrac{25k}{8}-211$.
 
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72 and 88
 
Yes, your answer is correct. Do you think you can share with MHB of your solution?
 

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