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MathNet 2021 — Part 04 Question 84

Math Olympiad Vault · MathNet 2021 — Part 04

Question 84

Let $n$ be the answer to this problem. $a$ and $b$ are positive integers satisfying
$$
\begin{aligned}
& 3 a+5 b \equiv 19 \quad(\bmod n+1) \\
& 4 a+2 b \equiv 25 \quad(\bmod n+1)
\end{aligned}
$$
Find $2 a+6 b$.