Question

Armstrong number is a number obtained summing the cubes of each number.....

consider the number to be abc

so took the eqn as

100a + 10b + c = a^3 + b^3 + c^3

how to solve this eqn???

Answer 1

There are an infinite number of possible solutions to that equation, but I suspect that's not quite what you're looking for...

Answer 2

I want to find the solution...
in what way can i approach it ??

Answer 3

Having googled "Armstrong Number", a better way to phrase that question is "An Armstrong number is a 3-digit number such that the sum of the cubes of each of its constituent digits is equal to the number itself. How can I find an armstrong number?"

Answer 4

Are you trying to find a general expression for all Armstrong numbers, or are you trying to simply find one Armstrong number?

Answer 5

yaa i know it is a 3 digit number....
i am trying to find the general expression and i want to find the total number of armstrong numbers present.

Answer 6

I realize that you know the definition. My point was that I did not, so what I said would have been a better way to ask the question in the first place.

Incidentally, you are restricting your attention to 3 digit numbers, then? Because the general concept of an Armstrong number can be applied to a number with any number of digits. If you are restricting yourself to 3 digit numbers, I don't think you can express a general relationship between the digits but it would be straightforward to systematically solve for them. There are only a handful.

Answer 7

if i can find the solution for this eqn ... then same procedure can be used to find it 4 or 5 or 6 digit number...

Answer 8

@hartn can u help me ???

Answer 9

You're asking for THE solution to an equation with MANY solutions. That is the primary problem here.

Answer 10

or at least SEVERAL.

Answer 11

@hartnn help me ??

Answer 12

@Jemurray3 cant we find that several numbers???

Answer 13

Yes, but I'm saying that you'd probably have to do it algorithmically rather than try to find a general expression for the digits. For instance, rearranging the equation,
\[100a-a^3 + 10b-b^3 + c-c^3 = 0\]
if a = 1 and b = 1,
\[99 + 9 = c^2- c \]
which doesn't yield an integer c... but going through this process, you might find that 153 works out just fine.

Answer 14

yaa i found that one...

i solve it like



i dont no to proceed further..

if i go by ur method it will be trial and error method..

so i am trying for some different approach.