How to delineate a summation of digits in a number? Let's say we have an integer x. How should I delineate a summation of its' digits until I get a single digit. For example: x = 12345 1 + 2 + 3 + 4 + 5 = 15 1 + 5 = 6 I believe it is possible, just can't find a mathematical way to do so. Would be glad if anyone shared their ideas or point me to the right direction.

What you're finding is called the **digital root** or **iterated digit sum**.

For positive $x$, the digital root is $9$ if $x$ is a multiple of $9$; otherwise it is the remainder of the division $x\div 9$.