Find base in which the number is a palindrome

1. Dec 25, 2009

tnutty

Sorry, this is not a H.W question . But I figure this is the more active section in math, and
that maybe some calculus can help.

The question is that given a number n, Find which base its a palindrome in.

For example,

The given number is n = 3. Starting from base 2 to x, we check which is the smallest base
its a palindrome in.

Starting from base 2.

(3)_10 = (11)_2 [ in base 2 ]
(3)_10 = (1)_3 [in base 3]
.. so on

But we see that base 2 is the smallest so we can stop there. Hope its clear enough.

The question I have is that, is there some theorem that states that a number N, is
palindrome in base > x, where x could be any number. Thus if we get a number N = 12323434. We done need to start checking from base 2. Instead we can start checking
from base x ( by some theorem). Sorry if this is a random question.