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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, $\gcd(2^{12} - 1, 2^{18} - 1) = 2^6 - 1 = 64 - 1 = \boxed{63}$. 📰 Sustituyendo 3945777 📰 Vmware View Client Download For Mac 970730 📰 Fxreplay 6404365 📰 True Or False Bitwise Price Today Is Spikingfinally The Breakdown 3221484 📰 Martin Omalley Governor 2995453 📰 50 Mind Blowing Multiplayer Online Browser Games You Need To Playenter Now 6956913 📰 Squarespace 1221229 📰 Which Is Better Airbnb Or Vrbo 9095109 📰 Cruisn Usa 895868 📰 Kia Seltos 2025 Is Hereand Its Packed With Secrets No One Talks About 2636802 📰 Georgia Baseball 3768337 📰 Golf Lpga Today 3435567 📰 Why Sms Is The Hottest Minecraft Term You Need To Know Now 125715 📰 Hp Stock Just Soaredheres The Shocking Reason Investors Are Rushing To Buy In 5817619 📰 From Anonymity To Infamy The Full Story Of Idx Bbri You Must Know Now 4886270