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Home » \[ \frac12 - \frac12 + c = 2 \] - AssociationVoting

\[ \frac12 - \frac12 + c = 2 \] - AssociationVoting

📅 May 17, 2026 👤 scraface

May 17, 2026

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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
Then $n = 36k = 36(7m + 3) = 252m + 108$.
We seek the smallest four-digit value of $n$:

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