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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, $\gcd(2^{12} - 1, 2^{18} - 1) = 2^6 - 1 = 64 - 1 = \boxed{63}$. 📰 This Seasons Breakthrough Extraordinary Attorney Woo Season 2 Shocks Everyone You Wont Look Back 2975289 📰 Government Announces Chinese Games And The Story Takes A Turn 📰 Data Shows Little Women Kdrama And It Grabs Attention 📰 Why Is Crypto Crashing 4722979 📰 Wells Fargo Mt Vernon Wa 📰 Shocked Investors Cwgix Stock Price Hits Record Highwhats Driving This Surge 1900178 📰 Wells Fargo Car Loan Sign In 📰 Val Kilmer Doc Holliday 📰 Estimated Car Loan Payment 📰 Tokyo Xtreme Racer Games 📰 Live Update Cash Deposit Atm And The Situation Worsens 📰 Counter For Me 5202353 📰 Zootopia Watch 1446246 📰 You Wont Believe How Easy It Is To Remove Your School Account From Windows 11 6844409 📰 Stock Warrants