Originally Posted by

**integerfan** is the question

302/20=12.1 proper?

i tried to take x as the base and trace the division algebraically:

( number 302 implies x>3 for the digit 3 appears in some number-----*inference 1*)

x + 2 + x^-1

----------------------------------

2x + 0 ) 3x^2 + 2

, :

, :

is what i expected to trace.

Following,

x

----------------------------------

2x + 0 ) 3x^2 + 2

, 2x^2

, ---------------

, x^2 comparing with ordinary arithmetic way,

x^2 must be lesser than 2x ( otherwise the quotient would be 2x or more ).

However, x^2 < 2x is true only when x=1 which is a contradiction with *inference 1*

what is going wrong here?

: