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How many bases $b$ are there such that $663_b$ is prime?

 Jul 15, 2019

Best Answer 

 #1
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How many bases $b$ are there such that $663_b$ is prime?   

 

Let "b" stand for any base.

 

663 = (6 x b2) + (6 x b) + 3  

 

the above can be written 6b2 + 6b + 3 

 

you can always factor a 3 out of 6b2 + 6b + 3

 

so, there is no base in which 663 is prime 

.

 Jul 16, 2019
 #1
avatar
+1
Best Answer

 

How many bases $b$ are there such that $663_b$ is prime?   

 

Let "b" stand for any base.

 

663 = (6 x b2) + (6 x b) + 3  

 

the above can be written 6b2 + 6b + 3 

 

you can always factor a 3 out of 6b2 + 6b + 3

 

so, there is no base in which 663 is prime 

.

Guest Jul 16, 2019

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