2022 SSMO Relay Round 3 Problems/Problem 3

Problem

Let $T=TNYWR$ . Let $f(x)$ be a polynomial of degree 10, such that $f(i)=i$ for all $i=1,2,\dots,10$ and $f(11) =T$ . Find the remainder when $f(13)$ is divided by $1000$ .

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2022 SSMO Relay Round 3 Problems/Problem 3

Problem

Solution