A positive integer is expressible as 3X1 in base B and 1X3 in base B+6, where X is a base B (and also base B+6) digit.

Find all values of B and X.

Prove that no further solution is possible.

*** Of course, B is a positive integer.

X=7, B=10    So  371=1*256+7*16+3=256+112+3

** does not merit d3

*** solved by comparing 3b^2 +b*x+1 and  (b+6)^2+(b+6)*x+3

Edited on May 2, 2016, 1:10 pm

Posted by Ady TZIDON on 2016-05-02 13:08:35