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What are primitive roots modulo n? - Mathematics Stack Exchange 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 $m\ge0$
Show that $2$ is a primitive root modulo $13$. Hence $2$ has order $12$ modulo 13 and is therefore a primitive root modulo $13$ Now note all even powers of $2$ can't be primitive roots as they are squares modulo $13$ $ (*)$
Finding a primitive root of a prime number 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
Understanding how Prime Polynomials are applied to LFSRs? To understand the connection between the taps and Primitive Polynomials, it is important to look into Galois Field or Finite field in depth However, I would try to summarise it: LFSR circuit basically performs multiplication on a "field"
Primitive binary necklaces - Mathematics Stack Exchange The problem solution of counting the number of (primitive) necklaces (Lyndon words) is very well known But what about results giving sufficient conditions for a given necklace be primitive? For ex
What is the integral of 1 x? - Mathematics Stack Exchange The absolute value sign is not necessary I mean, when we take an integral and want it to be meaningful, we usually take definite integral, not indefinite integral For $1 x$, the definite integral cannot be taken over an interval that contains 0, the two boundaries should be both positive or negative So $\int_a^b \frac {1} {x}dx=\log (b a)$, no mistake will be made
Primitive $p$-th root of unity with characteristic $p$ Leaving field theory again, if we consider the different complex roots of the polynomials $\alpha_i$ (excluding non-primitive root $1$, we would have $1\leq i \leq p-1$)