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bulgaria tst 2007

Source:

March 31, 2011
algebrapolynomialtrigonometryalgebra proposed

Problem Statement

i thought that this problem was in mathlinks but when i searched i didn't find it.so here it is: Find all positive integers m for which for all α,β∈Z−{0}\alpha,\beta \in \mathbb{Z}-\{0\} 2mαm−(α+β)m−(α−β)m3α2+β2∈Z \frac{2^m \alpha^m-(\alpha+\beta)^m-(\alpha-\beta)^m}{3 \alpha^2+\beta^2} \in \mathbb{Z}
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