+0

# i like pancakes

0
236
1
+638

If a and b must be positive integers, what is the largest integer n such that 13a + 18b = n has no solutions?

waffles  Aug 23, 2017
Sort:

#1
+92254
0

If a and b must be positive integers, what is the largest integer n such that 13a + 18b = n has no solutions?

I I don't know, I am getting really confused here . ://

This is what I am considering.

I used the euclidean algorithm, followed by the extended euclidean algorithm to come up with the generic solutions of

a= 7n-18k

b= -5n+13k

Where k is any integer.  So they are the answers to the diaphantine equation.   13a+18b=n

since a and be must both be positive

$$7n-18k>0\\ n>\frac{18k}{7}\qquad \qquad n>\frac{90k}{35} \\ -5n+13k>0\\ n<\frac{13k}{5}\qquad \qquad n<\frac{91k}{35} \\~\\ \frac{90k}{35} < n<\frac{91k}{35}$$

Mmm...   I have no idea where this is going.

Melody  Aug 23, 2017
edited by Melody  Aug 23, 2017
edited by Melody  Aug 23, 2017
edited by Melody  Aug 23, 2017

### 44 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details