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Home » Thus, there are $14$ such numbers. - inBeat

Thus, there are $14$ such numbers. - inBeat

📅 May 3, 2026 👤 scraface

May 03, 2026

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🔥 Popular Posts

To find the smallest four-digit number satisfying the given conditions...
\text{lcm}(12, 18) = \frac{12 \cdot 18}{\gcd(12, 18)} = \frac{216}{6}...
So, the number must be divisible by 36 and leave a remainder of 3 when...
n \equiv 0 \pmod{36}, \quad n \equiv 3 \pmod{7}
We solve this system using the Chinese Remainder Theorem. Since 36 and...
Let’s find $n$ such that:
Let $n = 36k$. Then:
36k \equiv 3 \pmod{7} \Rightarrow k \equiv 3 \cdot 36^{-1} \pmod{7}
Since $36 \equiv 1 \pmod{7}$, its inverse modulo 7 is 1. So:
k \equiv 3 \pmod{7} \Rightarrow k = 7m + 3

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