+0

# basemath

0
250
1
+2765

Suppose that $$b$$  is a positive integer greater than or equal to 2. When 197 is converted to base $$b$$ , the resulting representation has 4 digits. What is the number of possible values for b?

tertre  Mar 15, 2017

#1
+19653
+10

Suppose that is a positive integer greater than or equal to 2.

When 197 is converted to base b, the resulting representation has 4 digits.

What is the number of possible values for b?

$$\begin{array}{|rcll|} \hline 197_{10} &=& 11000101_2 \\ 197_{10} &=& 21022_3 \\ 197_{10} &=& 3011_{\color{red}4} \\ 197_{10} &=& 1242_{\color{red}5} \\ 197_{10} &=& 525_6 \\ 197_{10} &=& 401_7 \\ 197_{10} &=& 305_8 \\ 197_{10} &=& 238_9 \\ 197_{10} &=& 197_{10} \\ \cdots \\ \hline \end{array}$$

b is 4 or 5

heureka  Mar 15, 2017
#1
+19653
+10

Suppose that is a positive integer greater than or equal to 2.

When 197 is converted to base b, the resulting representation has 4 digits.

What is the number of possible values for b?

$$\begin{array}{|rcll|} \hline 197_{10} &=& 11000101_2 \\ 197_{10} &=& 21022_3 \\ 197_{10} &=& 3011_{\color{red}4} \\ 197_{10} &=& 1242_{\color{red}5} \\ 197_{10} &=& 525_6 \\ 197_{10} &=& 401_7 \\ 197_{10} &=& 305_8 \\ 197_{10} &=& 238_9 \\ 197_{10} &=& 197_{10} \\ \cdots \\ \hline \end{array}$$

b is 4 or 5

heureka  Mar 15, 2017