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Recent questions tagged finite-field

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CMI 2025 | Mathematics | Part B | Question: 18
Let $\mathbb{F}_{q}$ be the finite field with $q$ elements and $P \in \mathbb{F}_{q}[x]$ be a monic irreducible polynomial of even degree $2 d$. Then show that $P$, when ...
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CMI 2025 | Mathematics | Part A | Question: 3
Let $K$ be the splitting field of $X^{n}-1$ over $\mathbb{F}_{p}$, where $n$ is a positive integer. Pick the correct statement(s) from below.$K$ has $p^{n}$ elements.If $...
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CMI 2025 | Mathematics | Part A | Question: 4
Let $k$ be a finite field of characteristic $p>2$ and $G$ the subgroup of $\mathrm{GL}_{2}(k)$ consisting of all matrices whose first column is $\left[\begin{array}{l}1 \...
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TIFR Mathematics 2024 | Part A | Question: 17
Let $\mathbb{F}_{3}$ denote the finite field with 3 elements. What is the number of one dimensional vector subspaces of the vector space $\mathbb{F}_{3}^{5}$ over $\mathb...
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