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 $m\ge0$

Suppose that $r$ is not a primitive root modulo $p$, so there is some $b<p-1$ such that $r^b\equiv 1\bmod p$. In other words, there is some integer $t$ such that $r^b=1+pt$.

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 $13$. $ (*)$

How to find all primitive triples (a,b,c)? (Pythagorean Triples) Ask Question Asked 10 years, 8 months ago Modified 5 years, 9 months ago

I have to list the quadratic residues of $17$ and find a primitive root. I have calculated that: Quadratic residues $\\text{mod 17}$ are $1,2,4,8,9,13,15,16.$ How am I then meant to use this to obta...

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

Then, primitive recursive functions can be reduced to relations? And, in defining the p.r. functions he uses logical operators that i thought were available only inside the logical system. So, the domain of …

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 …

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 …

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...