May 16, 2023 · How would you find a primitive root of a prime number such as 761? How do you pick the primitive roots to test? Randomly? Thanks

This is false when $p=2$, since there is a primitive root modulo $2^2=4$, but no primitive root modulo $2^n$ for $n \geq 3$.

15 There is another example of a non-primitive-recursive but total computable function that explains better what the restricted definition of primitive recursion entails. Each primitive recursive function is …

The important fact is that the only numbers $n$ that have primitive roots modulo $n$ are of the form $2^\varepsilon p^m$, where $\varepsilon$ is either $0$ or $1$, $p$ is an odd prime, and $m\ge0$

Another method to show the "only if " direction is to use the fact that the trace of $\zeta_n$ is equal to zero if n is not square free, while by definition, the trace of $\zeta_n$ in this case is exactly the same …

Jan 6, 2019 · While antiderivative, primitive, and indefinite integral are synonymous in the United States, other languages seem not to have any equivalent terms for antiderivative. As others have pointed out …

Is this definition for primitive matrices correct? A square matrix $P \\geqslant 0$ is called primitive if there exists a power $k$ such that $P^k > 0,$ that is ...

9 What is a primitive polynomial? I was looking into some random number generation algorithms and 'primitive polynomial' came up a sufficient number of times that I decided to look into it in more detail. …

A nonnegative, irreducible matrix is primitive if and only if it is aperiodic (ibid. Theorem 8.5.3). According to this source, we wouldn't ever call a reducible matrix primitive. Though a reducible matrix can still …

Jul 23, 2018 · 6 So I encountered this proof on a Number Theory book, I will link the pdf at the end of the post (proof at page 96), it says: " Every prime has a primitive root, proof: Let p be a prime and let m …