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Cubic Equation (
Posted on 20130609
)
Determine all triplets (a,b,c) of
nonzero integers
satisfying:
987654321*a + 123456789*b + c = (a + b + c)
^{3}
Prove that there are no others.
No Solution Yet
Submitted by
K Sengupta
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Another solution (spoiler)
 Comment 2 of 13 
Charlie's done all the hard work.
Clearly, another solution is (a,b,c) = (450,4500,5050)
We might be able to prove that these are unique by letting
a = 450 + X
b = 4500 + y
c = 5050 + z
but the math still looks difficult
Or maybe doing something mod 450 would work ...
Posted by
Steve Herman
on 20130609 19:46:22
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