perplexus.info :: Just Math : Cubic Equation

Cubic Equation (Posted on 2013-06-09)

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 2013-06-09 19:46:22

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