+0

# find the base of numeration in which 135/21 has a zero remainder

0
47
1

find the base of numeration in which 135/21 has a zero remainder

Guest Feb 7, 2018

#1
+91795
+2

find the base of numeration in which 135/21 has a zero remainder

Let the base be x

$$\frac{x^2+3x+5}{2x+1}=n \qquad n\in Z\\$$

I am going to try trial and error.

x has to be 6 or bigger because of the 5.

If x=6 this becomes

$$\frac{36+16+5}{13}=\frac{57}{13}\ne n$$

If x=7

$$\frac{49+21+5}{14+1}=\frac{75}{15}=5=n$$

So base 7 works

Melody  Feb 7, 2018
Sort:

#1
+91795
+2

find the base of numeration in which 135/21 has a zero remainder

Let the base be x

$$\frac{x^2+3x+5}{2x+1}=n \qquad n\in Z\\$$

I am going to try trial and error.

x has to be 6 or bigger because of the 5.

If x=6 this becomes

$$\frac{36+16+5}{13}=\frac{57}{13}\ne n$$

If x=7

$$\frac{49+21+5}{14+1}=\frac{75}{15}=5=n$$

So base 7 works

Melody  Feb 7, 2018

### 11 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