On the multiplicative order of the roots of $bX^{q^r+1}-aX^{q^r}+dX-c$

In this paper, we find a lower bound for the order of the group $\langle \theta+\alpha\rangle \subset \overline{\mathbb F_{q}}^* $, w h e r e$ \alpha\in \mathbb F_{q} $,$ \theta $i s a g e n e r i c r o o t o f t h e p o l y n o m i a l$ F_{A,r}(X)=bX^{q^r+1}-aX^{q^r}+dX-c\in \mathbb F_{q}[X] $a n d$ ad-bc\ne0$.

On the multiplicative order of the roots of $b X^{q^{r} + 1} - a X^{q^{r}} + d X - c$

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On the multiplicative order of the roots of $b X^{q^{r} + 1} - a X^{q^{r}} + d X - c$

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On the multiplicative order of the roots of bXqr+1−aXqr+dX−cbXqr+1−aXqr+dX−c

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On the multiplicative order of the roots of bXqr+1−aXqr+dX−cbXqr+1−aXqr+dX−c

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On the multiplicative order of the roots of $b X^{q^{r} + 1} - a X^{q^{r}} + d X - c$

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On the multiplicative order of the roots of $b X^{q^{r} + 1} - a X^{q^{r}} + d X - c$

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AI智能校验