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.