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

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The discussion focuses on solving the equation for positive integers \( k \) where the product of the digits of \( k \) equals \( \frac{25k}{8} - 211 \). The confirmed solutions are \( k = 72 \) and \( k = 88 \). Participants validate these solutions and encourage sharing the methodology on the Math Help Boards (MHB). The problem highlights the relationship between digit products and linear equations.

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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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