Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
I just discovered something which I am unable to prove.
Any natural number \(n\) can be represented as a multiple of 9 + Sum of the digits of \(n\).
 one year ago
 one year ago
I just discovered something which I am unable to prove. Any natural number \(n\) can be represented as a multiple of 9 + Sum of the digits of \(n\).
 one year ago
 one year ago

This Question is Closed

ParthKohliBest ResponseYou've already chosen the best response.0
For example: 9 = 0 + 9 40 = 36 + 4 + 0 120 = 117 + 2 + 0
 one year ago

waterineyesBest ResponseYou've already chosen the best response.1
I got you but 120 = 117 + 1 + 2 + 0
 one year ago

waterineyesBest ResponseYou've already chosen the best response.1
45 = 45 + 4 + 5 ???
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.0
No, 45 = 36 + 4 + 5
 one year ago

waterineyesBest ResponseYou've already chosen the best response.1
Kidding: 45 = 36 + 4 + 5
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.0
Do you use induction to prove?
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.0
what about the numbers below 9?
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.0
0 is a multiple of 9. 9 * 0 = 0
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.0
isnt that cheating lol? everything is a multiple of zero then
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.0
But I need to prove this thing. How do you do that?
 one year ago

waterineyesBest ResponseYou've already chosen the best response.1
98 = 90 + 9 + 8 ???
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.0
more like 81 + 9 + 8
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.0
How do you prove it?
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.0
\[\text{decimal} \]
 one year ago

Mimi_x3Best ResponseYou've already chosen the best response.1
Can you use Mathematical Induction to prove that? lol
 one year ago

waterineyesBest ResponseYou've already chosen the best response.1
He is saying natural number @UnkleRhaukus
 one year ago

Mimi_x3Best ResponseYou've already chosen the best response.1
I don't think so Parth; you can't prove that with MI, not certain though.
 one year ago

waterineyesBest ResponseYou've already chosen the best response.1
I guess, Mukushla will give something to cheer upon..
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.0
i have a feeling it has something to do with mods
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.0
our number system is to base 10
 one year ago

mukushlaBest ResponseYou've already chosen the best response.2
sorry i lost my connection if n is a m+1 digit number \( n=(a_{m}a_{m1}....a_{1}a_{0})=10^m a_{m}+10^{m1} a_{m1}+...+10a_{1}+a_{0} \) now \( n(a_{m}+a_{m1}+...+a_{1}+a_{0})=(10^m 1)a_{m}+(10^{m1}1)a_{m1}+...+9a_{1}=9k \)
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.0
I got a proof, finally. \( \color{Black}{\Rightarrow \bar{abc} = 100a + 10a + c }\) \( \color{Black}{\Rightarrow 99a + a + 9b + b + c}\) \( \color{Black}{\Rightarrow 9(11a + b) + (a + b + c)}\) 11a + b is a multiple of 9.
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.0
Is my proof good enough?
 one year ago

mukushlaBest ResponseYou've already chosen the best response.2
@ParthKohli u did my work for m=2
 one year ago

waterineyesBest ResponseYou've already chosen the best response.1
\((10^k  1)\) will be multiple of 9 always..
 one year ago

mukushlaBest ResponseYou've already chosen the best response.2
@waterineyes thats right
 one year ago

waterineyesBest ResponseYou've already chosen the best response.1
My guess is right: Mukushla has given something to cheer upon..
 one year ago
See more questions >>>
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.