Number Theory

 

Find the number of bases $b \ge 2$ such that $100_b - 1_b$ is prime.    

 

The third position to the left is the base raised to the second power position.    

 

So this problem could be viewed as "For which bases "b" can (b² – 1) be prime?"    

 

The only base I could find for which this works is 2 ... i.e., 2² – 1 = 3.    

 

Therefore, the answer to the problem is:  there is only one.    

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