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Difference between revisions of "2022 SSMO Relay Round 4 Problems/Problem 3"

(Created page with "==Problem== Let <math>T=</math> TNYWR. If <math>f(1)=1</math>, <math>f(2)=12</math>, and<cmath>f(n+2)=12f(n+1)-20f(n)</cmath>for all positive integers <math>n</math>, find the...")
 
 
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==Problem==
 
==Problem==
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Let <math>T=</math> TNYWR. If <math>f(1)=1</math>, <math>f(2)=12</math>, and<cmath>f(n+2)=12f(n+1)-20f(n)</cmath>for all positive integers <math>n</math>, find the remainder when <math>f(T)</math> is divided by <math>1000.</math>
+
Let <math>T=TNYWR</math>. If <math>f(1)=1</math>, <math>f(2)=12</math>, and<cmath>f(n+2)=12f(n+1)-20f(n)</cmath>for all positive integers <math>n</math>, find the remainder when <math>f(T)</math> is divided by <math>1000.</math>
  
 
==Solution==
 
==Solution==

Latest revision as of 19:22, 2 May 2025

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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