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📰 Question: What two-digit number is three more than a multiple of 7 and five more than a multiple of 6? 📰 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 $\boxed{17}$. 📰 Cowz Stock Explosion Are These Shape Shifting Cows Takeover The Market 8396805 📰 A Scientist Is Observing The Growth Of Bacteria In A Petri Dish Initially There Are 1000 Bacteria The Population Doubles Every 3 Hours After 24 Hours How Many Bacteria Are Present In The Dish 1347597 📰 Tde Artists 📰 Voice Recorder App For Mac 📰 Unbelievable Hudl Breakdown You Wont Believe Hauts 42818 📰 Bank Of America In Jackson Heights 9036640 📰 Steam Trails In The Sky 📰 Aja System Test Lite 📰 Read Read Read Past Tense 6133325 📰 She Posted A Clip That Drove Thousands To Scroll Past Her Accountwhat Happened Next Shocked Everyone 7721350 📰 Realtor Pro Secrets You Need Crush The Market And Close Big Deals Fast 5895721 📰 Death And Taxes Game 📰 Lost Eidolons 9496970 📰 Saving Account Promos 📰 Usd To Uzs Rate Current