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There are an infinite number of possible solutions to that equation, but I suspect that's not quite what you're looking for...
I want to find the solution... in what way can i approach it ??
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?"
Are you trying to find a general expression for all Armstrong numbers, or are you trying to simply find one Armstrong number?
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.
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.
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...
@hartn can u help me ???
You're asking for THE solution to an equation with MANY solutions. That is the primary problem here.
or at least SEVERAL.
@hartnn help me ??
@Jemurray3 cant we find that several numbers???
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.
yaa i found that one... i solve it like |dw:1348380805812:dw| 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.
If you code a program you could do it in about ten seconds...
def Armstrong(): for i in range(1,9): for j in range(0,9): for k in range(0,9): if i*i*i + j*j*j + k*k*k == 100*i + 10*j + k: print(100*i+10*j+k)
I'm serious. This is a perfect example of when a computer program would be wonderful. The above code took a little over 10 seconds to write and produced the four 3-digit Armstrong numbers.
@Jemurray3 thank u