# Find base in which the number is a palindrome

• tnutty
In summary, the conversation discusses the question of finding the smallest base in which a given number is a palindrome. The speaker suggests using calculus to solve this problem and asks if there is a theorem that states a number is a palindrome in any base greater than a given number. However, it is clarified that there is no such theorem and the only way to determine if a number is a palindrome in a given base is by converting it to that base and checking.
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.

No, there is no such theorem. The only way to determine if a number is a palindrome in a given base is to convert it to that base and check if the resulting number is a palindrome. There is no shortcut or general formula to determine this without first converting the number to the given base.

## 1. How do you determine if a number is a palindrome?

To determine if a number is a palindrome, you need to reverse the order of its digits and compare it to the original number. If they are the same, then the number is a palindrome.

## 2. What is the base in which a number is considered a palindrome?

The base does not affect whether a number is a palindrome or not. A number can be a palindrome in any base, as long as its digits are read in the same order forwards and backwards.

## 3. Can a negative number be a palindrome?

No, a negative number cannot be a palindrome because the negative sign changes the order of the digits.

## 4. How do you find the base in which a given number is a palindrome?

To find the base in which a given number is a palindrome, you can use trial and error by converting the number to different bases until you find one where the number is a palindrome. Alternatively, you can use mathematical algorithms to determine the base.

## 5. Are there any shortcuts or tricks to finding the base in which a number is a palindrome?

Yes, there are some shortcuts and tricks that can be used to find the base in which a number is a palindrome. For example, if the number is a perfect square, then it will always be a palindrome in base 10 and its square root will be the base in which it is a palindrome.

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