A two-digit base 7 positive integer has its digits reversed when expressed in base N.

What are the possible values of N satisfying the given conditions?

let b be the base:

7x+y=b*y+x

6x=(b-1)*y     eq1

base 3:   12 b7  is 21 ternary

base 5:   23 b7  is  32  b5

 base 10:   32 b7  is  23  b10    and  64 b7  is   46  b10

base 13:   21==>12;   42==>24;    63==>36; 

base 16:  52==>25; 
base 19:  31==>13;   62==>26;

highr bases may comply with the equation eq1, but introduce digits higher than 6.

So se are left with bases 3,5,10,13,16,19

Posted by Ady TZIDON on 2014-10-15 11:44:41