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Solving the diophantine equation:\[a^3 + b^3 + c^3 = 100a + 10b + c \]

Mathematics
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hmmm
Can you help me with that?
find all integer solutions

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Other answers:

looks like we can factor something here
did you try to expand (a+b+c)^3
Whoo.
\[a^3+3 a^2 b+3 a^2 c+3 a b^2+6 a b c+3 a c^2+b^3+3 b^2 c+3 b c^2+c^3\]
So do we have to add \(3 a^2 b+3 a^2 c+3 a b^2+6 a b c+3 a c^2+3 b^2 c+3 b c^2\) to both sides?
\[(a + b + c)^3 = 3 a^2 b+3 a^2 c+3 a b^2+6 a b c+3 a c^2+3 b^2 c+3 b c^2 + 100a + 10b + c \]
oh look at that
one second
(a+b+c)^3 = a^3+3 a^2 b+3 a^2 c+3 a b^2+6 a b c+3 a c^2+b^3+3 b^2 c+3 b c^2+c^3
How would you solve it now?
not sure
where did you get this question, is it solvable?
well the simple approach is , equate terms
Yes, a solution is \((1,5,3)\)
|dw:1360413980599:dw|
so if a^2 = 100 , b^2 = 10 , and c^2 = 1 , you have a solution
I didn't mention that \((a,b,c)\) all must be single-digit numbers.
ok, then you can go through all the cases , 0-9
I want a purely mathematical solution :-|
Not by guesses...

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