# What is Sum of digits: Definition and 15 Discussions

In mathematics, the digit sum of a natural number in a given number base is the sum of all its digits. For example, the digit sum of the decimal number

9045

{\displaystyle 9045}
would be

9
+
0
+
4
+
5
=
18

{\displaystyle 9+0+4+5=18}
.

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1. ### MHB Finding 3-Digit Numbers with Sum of Digits Squared = 2

For any natural number $n$, let $S(n)$ denote the sum of the digits of $n$. Find the number of all 3-digit numbers $n$ such that $S(S(n))=2$.
2. ### B Quickest way to calculate a given summation

How would you, personally, do this summation the quickest way?
3. ### Discovering the Formula for Σ (i=1, n) √i

Homework Statement Calculate Σ (i=1, n) √i I want to write general formula, then use it for any n (like we have for Σ (i=1, n) i Homework Equations Σ (i=1, n) i = n (n+1) / 2 Σ (i=1, n) i^2 = n (n+1)(2n +1) / 6The Attempt at a Solution Comparing formulas provided above: I assume the answer...
4. ### Pascal - absolute sum of digits

Homework Statement Make an "absolute sum of digits" of a number in a particular numerical system. You are given two numbers (numerical system and your number N). You take the number N, add up its digits, if the result has more than one digit you add them up again and so on. You end up with...
5. ### Pascal - sum of digits in binary/hexadecimal

Homework Statement Read two integers. First one tells you the type of your numeral system (binary, decimal, hexadecimal) the second one will be your number in decimal. Using functions or procedures I need to convert the number into the required system and then count the sum of its digits in...
6. ### Formula for sum of digits of a number

Any ideas on this? I googled it and got only answers inolving Excel, C++, etc... A formula for finding the digit sum of a 2-digit number, or only a 3-digit number, would also be interesting. I thought I had a start with this: For a 2-digit number xy, the sum of the digits =...
7. ### Number minus sum of digits is dividable by 9

Hello! Why is it so, that if you have a number, for example 183, you take the sum of the digits of that number, so 183-(1+8+3), u get a number that is always dividable by 9? I'm sorry if this is a dumb question, I'm not very good at math but still curious to know.
8. ### Sum of digits without regard to place value?

I apologize for my lack of knowledge on the topic. I recently started writing programs to solve Project Euler problems and it rekindled my interest in number theory. Especially as it relates to a peculiar relationship I found back in high school. I would like to learn more about number theory...
9. ### Divisibility rules using sum of digits

I saw someone discussing divisibility rules in another thread and would thought I would make a note that the divisibility rule of 9 of summing the digits to see if you end up with 9 is really a trick of the counting base you are using (base 10). In general, this divisibility rule applies to...
10. ### What is the sum of digits in the numbers 1 to 2010?

Determine the sum of all the digits in the positive integers from 1 to 2010 inclusively.
11. ### Bus ticket and sum of digits puzzle

Yesterday Professor Q rode on a bus with his friend. As soon as he got the tickets for himself and his friend, which were consecutively numbered with each of the tickets bearing a 5-digit number with no leading zero, he added the digits on them and told his friend that the sum of all ten digits...
12. ### What is the Sum of Digits for 2^1000?

What is the sum of the digits of 2^1000 check my algoriathm, let y=2^1000 then logy = 1000log2 = 301 and y=10^logy=10^301 since (1,0) r da only digits of 10^n 4all n=1,2,3,4,... The sum of digits equals 1 , but it is not the answer ...Why?
13. ### Urgend: Sum of digits question

I have question here which has puzelled me since monday. Hope there is somebody here who can give a hint/help. Let "a" be number written in base 10. a_0 * 10^0 + a_1 * 10^1 + a_2 * 10^2 + -------+ a_n * 10^n where 0 \leq a_i \leq 10. Prove that the number 2 divides a, if and only...
14. ### Is the Sum of Digits Always Nine?

I don't know if this has been posted already, but anwho... If you pick any positive integer greater than 9 and subtract the sum of its digits from that number, you'll end up with a multiple of 9. How do I know it's a multiple of 9? Curiously enough, the sum of the digits of a positive integer...
15. ### Can f(n) equal f(x) in the sum of digits equation?

"sum of digits" equation Let f(n) denote the sum of (all) digits of natural number n. Prove that for each natural n we can choose convenient value of natural parameter p such that the equation f(npx)=f(x) has solution in natural numbers x that doesn't contain any "9" in its notation. Does...