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2022 SSMO Relay Round 4 Problems/Problem 3

Problem

Let $T=$ TNYWR. If $f(1)=1$, $f(2)=12$, and\[f(n+2)=12f(n+1)-20f(n)\]for all positive integers $n$, find the remainder when $f(T)$ is divided by $1000.$

Solution

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