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πŸ“° Question: What two-digit number is three more than a multiple of 7 and five more than a multiple of 6? πŸ“° Solution: Let the number be $n$. Then $n \equiv 3 \pmod{7}$ and $n \equiv 5 \pmod{6}$. Solve the system: πŸ“° 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 $\boxed{17}$. πŸ“° 1 American Dollar To 1 Australian Dollar πŸ“° Pollys Breakthrough How One Small Name Sparked A Massive Trend 7359582 πŸ“° To Ask In Spanish 5896096 πŸ“° Kwd To Dollar 1280828 πŸ“° Lounah Caf 6005166 πŸ“° Big Announcement Outer Worlds 2 Endings And The Reaction Is Immediate πŸ“° Anger Management Movie That Will Made You Lose Controlshockingly Real 1619379 πŸ“° Patagonia Stock πŸ“° Chart Usd Rmb 7637349 πŸ“° This Restaurant Review App Reveals The Best And Worst Spots You Cant Miss 6873655 πŸ“° Dice Coefficient πŸ“° Cafe Luka Manhattan 4825764 πŸ“° Prparer Le Contenu Craquant Pour Baldurs Gate 3 Ps5 Click To Explore The Best Moments 9653230 πŸ“° Weather Castro Valley 5312902 πŸ“° The Ultimate Mmo Champion Breakthrough Everyone Is Reporting On Mmo Champion 9251286