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Your polynomial is primitive, which means that the order of $x$ modulo your polynomial is exactly $2^{15}-1$. In particular, $x^a \not\equiv 1$ modulo your polynomial for all $1 \leq a \leq 2^{15}-2$, which means that your polynomial doesn't divide $x^a-1$ for this range of $a$. (This also means that your polynomial should divide $x^{2^{15}-1}-1$, in ...

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