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Home » birthstone color for the month of september - Anadea

birthstone color for the month of september - Anadea

📅 May 17, 2026 👤 scraface

May 17, 2026

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4k \equiv 1 \pmod{7}
Multiplying both sides by the modular inverse of 4 modulo 7, which is...
k \equiv 2 \pmod{7}
So $k = 7m + 2$. Then $x = 60k = 60(7m + 2) = 420m + 120$. We seek the...
x = 420m + 120 \geq 100 \Rightarrow m \geq 0
Try $m = 0$: $x = 120$ (valid, three-digit). Check $120 \mod 7 = 1$?
\div 7 = 17 \text{ remainder } 1 \Rightarrow \text{Yes}
Thus, the smallest such number is $\boxed{120}$.
Question: What is the largest integer that must divide the product of...
Solution: Let the four consecutive odd integers be $n, n+2, n+4, n+6$,...

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