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?
 
Thread 'Erroneously finding discrepancy in transpose rule'

Thread 'Erroneously finding discrepancy in transpose rule'

Obviously, there is something elementary I am missing here. To form the transpose of a matrix, one exchanges rows and columns, so the transpose of a scalar, considered as (or isomorphic to) a one-entry matrix, should stay the same, including if the scalar is a complex number. On the other hand, in the isomorphism between the complex plane and the real plane, a complex number a+bi corresponds to a matrix in the real plane; taking the transpose we get which then corresponds to a-bi...
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