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Are there infinitely many integers $ n>0$ at which a $ 0$ and $ \pm1$ coefficient polynomial $ f(x)$ that divides $ x^{n^\beta}-1$ with degree $ n^{\beta}-O(n^{\alpha})$ and number of non-zero coefficients $ n^\beta-\omega(n^{\alpha + \epsilon})$ at any $ \beta>\alpha$ and fixed $ \alpha>2$ and $ \epsilon>0$ exists?Read more