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