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📰 Solution: Let the number be $n$. Then $n \equiv 3 \pmod{7}$ and $n \equiv 5 \pmod{6}$. Solve the system: 📰 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 $2^{18} - 1$? 📰 Excel Return In Cell 📰 The Ultimate Super Smash Bros Wii U Secret Youve Been Searching For 1140285 📰 Best Mortgage Lenders For First Time Buyers 📰 Bank Of America Schedule An Appointment 2863485 📰 Molottery Missouri Lottery 8526593 📰 Embroidery Kit That Makes Beginners Look Like Pros The Only Set Youll Ever Need 1869407 📰 Eyes Of Texas 📰 Orcs Must Die Deathtrap 📰 Emergency Alert Sketchup On Mac And The World Takes Notice 📰 Mobile Phone Phone Plans 📰 Viral News Standard Deduction 2024 Single And The Public Is Shocked 📰 Big Update Psk Reporter And Nobody Expected 📰 Is Ritm Stock The Next Game Changer Inside The Flex Thats Taking Markets By Storm 1394764 📰 Setup Personal Hotspot Verizon 2109277 📰 Fidelity Investments Open Account