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> | + | 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 . Let
be a polynomial of degree 10, such that
for all
and
. Find the remainder when
is divided by
.