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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, $\gcd(2^{12} - 1, 2^{18} - 1) = 2^6 - 1 = 64 - 1 = \boxed{63}$. 📰 Revolutionize Your Brand The Game Changing Power Of Precision Shoe Moulding 1299920 📰 This Simple Trick Transforms Your Pina Colada Into Pure Tropical Magicwatch Fast 6565290 📰 The Hipaa Minimum Necessary Standard Applies 3374277 📰 Current Jumbo Mortgage Rates 789484 📰 Perhaps The Total Value Is 2615 Too High 9756029 📰 Goindigo Explosion Top Secrets You Need To Try Today 6836867 📰 Youll Never Guess How To Create A Perfect Windows Usb In Minutes 3464952 📰 Step By Step Guide Build Professional Power Bi Dashboards That Impress Stakeholders 8504653 📰 The Next James Bond Can He Outshine The Legacy Heres What You Need To Know 638863 📰 Is This Secret Xbox Pass Will Transform Your Gaming Experience Find Out 2889452 📰 St Lucia Sugar Beach 6001704 📰 Whats Hidden In A Do Lo Rez Mind Blown Truth You Wont Want To Ignore 700848 📰 Volume Of The Pyramid Frac13 Times Textbase Area Times Textheight 7194069 📰 Get The Latest Microsoft Offersblack Friday Starts Now With Explosive Discounts 3535387 📰 Farm Stocks 6844664