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Results tagged with finite-fields
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user 89000
A finite field is a field with a finite number of elements. For each prime power $q^k$, there is a unique (up to isomorphism) finite field with $q^k$ elements. Up to isomorphism, these are the only finite fields.
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Invariant complementary sets modulo $p$
Let $p \ge 11$ be a prime number, $k,n$ be positive integers such that $n|gcd(p-1,k-1)$ and $p > k > n \ge 5$. Let $s \in \mathbb Z_p$ such that $ord_p(s) = n$. Is it possible that the sets $A = \{1,2 …
- 169
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Geometric progression modulo p [closed]
Let $p\ge 11$ be a prime number, $n \ge 5$ be an odd positive divisor of $p-1$ and $s \in \mathbb Z_p$ such that $ord_p(s) = n$.
Is it true that the geometric progression $\{s^k\}_{k \in \mathbb Z_n} …
- 169
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Number of classes $\pmod p$ represented by $b_1s^{n-1} + \dots + b_n$ where $ord_p(s) = n$
Let $n \in \mathbb Z$ with $n \ge 3$ and let $p$ be a prime number such that $n|p-1$. Let $a_1,a_2,\dots,a_{2n-1} \in \mathbb Z/p\mathbb Z$. Suppose that the same class is represented by at most $n-1$ …
- 169