digitsumn

Digitsumn is a mathematical operation that involves summing the individual digits of a number. For example, the digitsumn of 123 is 1 + 2 + 3 = 6. This operation is often used in number theory and recreational mathematics.

The digitsumn of a number is equivalent to the number modulo 9, with the exception that if the number is a multiple of 9, its digitsumn is 9 (whereas the number modulo 9 would be 0). This property arises from the fact that any power of 10 is congruent to 1 modulo 9. For instance, 10 = 9 + 1 ≡ 1 (mod 9), 100 = 99 + 1 ≡ 1 (mod 9), and so on. Therefore, a number like abc (which can be written as 100a + 10b + c) is congruent to a(1) + b(1) + c (mod 9), which is the sum of its digits.

The digitsumn is also known as the digital root when the process is repeated until a single digit is obtained. For example, the digitsumn of 987 is 9 + 8 + 7 = 24. The digitsumn of 24 is 2 + 4 = 6. Since 6 is a single digit, it is the digital root of 987. The digital root of any non-negative integer can be found by repeatedly applying the digitsumn operation until a single-digit number is reached. This single-digit number is always between 1 and 9, inclusive.