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

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

Guest Feb 7, 2018

#1
+94183
+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
#1
+94183
+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