INMO 2021
The proof is now complete. Alternate Solution. The only such pair is (0;0), which clearly works. Let us prove this is the only one. In what follows, we use 2(n) to denote the largest integer kso that 2kjn for any non-zero n2Z. If one of the cubics has 0 as a root, say the first one, then 03 + 0 a+ b= 0, so b= 0.
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