An integer n written in base b is 211 and 110
written in base b+2. Find n and b in base 10.   

Comparing    2* b^2+b+1 with (b+2)^2+b+2

We get   b^2-4b-5=0   i.e. (b-5)*(b+1)=0

Solving it    b=5   n=56

b=-1  is  n.a. (even if negative base was allowed, there would be no digit 2 in it)

 

Posted by Ady TZIDON on 2016-03-17 11:19:24