Difference between revisions of "2022 SSMO Relay Round 3 Problems/Problem 3"

(Created page with "==Problem== Let <math>T=</math> TNYWR. Let <math>f(x)</math> be a polynomial of degree 10, such that <math>f(i)=i</math> for all <math>i=1,2,\dots,10</math> and <math>f(11) =T...")
 
 
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==Problem==
 
==Problem==
Let <math>T=</math> TNYWR. Let <math>f(x)</math> be a polynomial of degree 10, such that <math>f(i)=i</math> for all <math>i=1,2,\dots,10</math> and <math>f(11) =T</math>. Find the remainder when <math>f(13)</math> is divided by <math>1000</math>.
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Let <math>T=TNYWR</math>. Let <math>f(x)</math> be a polynomial of degree 10, such that <math>f(i)=i</math> for all <math>i=1,2,\dots,10</math> and <math>f(11) =T</math>. Find the remainder when <math>f(13)</math> is divided by <math>1000</math>.
  
 
==Solution==
 
==Solution==

Latest revision as of 19:24, 2 May 2025

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 $1000$.

Solution