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📰 From $n \equiv 5 \pmod{6}$, $n = 6k + 5$. Substitute into the first congruence: $6k + 5 \equiv 3 \pmod{7} \Rightarrow 6k \equiv -2 \pmod{7} \Rightarrow 6k \equiv 5 \pmod{7}$. Multiply both sides by the modular inverse of 6 mod 7 (which is 6, since $6 \times 6 = 36 \equiv 1 \pmod{7}$): $k \equiv 5 \times 6 \equiv 30 \equiv 2 \pmod{7}$. Thus, $k = 7m + 2$, and $n = 6(7m + 2) + 5 = 42m + 17$. The two-digit solutions are when $m = 0$: $n = 17$ and $m = 1$: $n = 59$. The smallest is $\boxed{17}$. 📰 Question: What is the greatest common divisor of $2^{12} - 1$ and $2^{18} - 1$? 📰 Solution: Use the identity $\gcd(2^a - 1, 2^b - 1) = 2^{\gcd(a, b)} - 1$. Compute $\gcd(12, 18) = 6$. Thus, $\gcd(2^{12} - 1, 2^{18} - 1) = 2^6 - 1 = 64 - 1 = \boxed{63}$. 📰 Why 367 Is The Key To Unlocking Intense Heatno One Saw This Coming 7429377 📰 Henry Winkler Net Worth 7039395 📰 Aurrasing 6842524 📰 Table A Roulettes Explored The Secret Strategy Every Casino Love 3585154 📰 Cleanflowers Murder Shoes Why Every Cleaners Feet Are Hiding Something 5574645 📰 Ir Examiner 4449518 📰 2025S Biggest Ai Revolution Join Microsofts Fest And Unlock Top Microsoft Ai Skills Now 843797 📰 Patriots Game This Weekend 2218361 📰 Shocked By The Olde Pink House Menuthis Hidden Gem Exploded Online 5700 📰 Revealed The Hidden Total War Strategy Behind Star Wars Rogue Wars 4010278 📰 United States Dollar To Australian Dollar 2303161 📰 Jessika Nicole 1299775 📰 You Wont Believe What This Retro Game Boy Caught Up Togame Boy Secrets Revealed 3246083 📰 Process Monitor Sysinternals 1713439 📰 Arched Back 5260397