To get a number’s palindrome in a programming language like python is easy. There are ways to swap between integer and string and strings can be manipulated.

```
>>> n = 1234
>>> int(str(n)[::-1])
4321
```

But I wanted to create a mathematical function , which returns an integer’s palindrome. Thus .

Firstly I needed a way of determining the number’s size. In base the length is calculated using the logarithm to said base.

Secondly I need a way to isolate a specific digit. Using the floor function, this function returns the digit (starting on the right with ).

Thirdly both of these functions can be used to split up the number into a sum.

Fourthly I only need to swap the power of ten at the end to get my palindrome function.

Thus the final function is defined.

To check if the formula is correct, I use (as seen above).