Observation: for any 3 integers, x,y,z, the product of their cubes is a perfect cube; (x^3)(y^3)(z^3) = (xyz)^3
Conjecture: that for integers a,b,c, their cube roots can only be in arithmetic sequence if all 3 cube roots are integers.
I'm not certain that the conjecture is true, but if it is then it would be sufficient for a proof.
But proving the conjecture might be more difficult than proving the original problem, particularly since the conjecture may be wrong.
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Posted by Larry
on 2024-12-07 15:13:02 |
First thoughts: a conjecture
