Question 1.2. Determine the smallest no € No such that n is a sum of 5's and 9's, for all integersn no. Prove your answer.

To find:The smallest such that is a sum of and , for all integers .Concept used:The concept of…

Answered: Question 1.2. Determine the smallest no…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Expert Solution

Step 1: Introduction

To find:

The smallest $n subscript 0 element of straight natural numbers subscript 0$ such that $n$ is a sum of $5 apostrophe text s end text$ and $9 text 's end text$ , for all integers $n greater or equal than n subscript 0$ .

Concept used:

The concept of the Chicken McNugget Theorem (also known as the Frobenius Coin Problem) to solve this problem.

Formula used:

The Chicken McNugget theorem states that for any two relatively prime positive integers $a$ and $b$ (meaning they have no common factors other than $1$ ), the largest integer that cannot be expressed as a linear combination of $a$ and $b$ is given by:

$text N end text open parentheses a comma b close parentheses equals open parentheses a cross times b close parentheses minus a minus b$