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Home » $T_n = S_n-1$ (append 2 to a string ending in 3) - AMAZONAWS

$T_n = S_n-1$ (append 2 to a string ending in 3) - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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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 $n, n+2, n+4, n+6$,...
P = n(n+2)(n+4)(n+6)

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