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Homework Help: Find base in which the number is a palindrome

  1. Dec 25, 2009 #1
    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.
  2. jcsd
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