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📅 May 17, 2026 👤 scraface

May 17, 2026

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\( k \) is divisible by the sum of its digits.
Let \( k = 10a + b \), where \( a \in \{1,2,\dots,9\} \), \( b \in \{0...
We check two-digit numbers \( k \equiv 2 \pmod{7} \): they are:
k = 16, 23, 30, 37, 44, 51, 58, 65, 72, 79, 86, 93
Now test each for divisibility by digit sum:
\( k = 16 \): digit sum = \( 1+6 = 7 \), \( 16 \div 7 \approx 2.28 \),...
\( k = 23 \): sum = \( 2+3 = 5 \), \( 23 \div 5 = 4.6 \), no.
\( k = 30 \): sum = \( 3+0 = 3 \), \( 30 \div 3 = 10 \), yes!
So \( k = 30 \) is divisible by digit sum (3), and \( 30 \div 7 = 4 \t...
Thus, the smallest such two-digit number is:

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