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 …

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 $13$. $ (*)$

Here's a proof showing why Ackermann's function is not primitive recursive. The key to showing that A is not primitive recursive, is to find a properties shared by all primitive recursive …

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 …

Wikipedia has the result that Gauss proved that for a prime number $p$ the sum of its primitive roots is congruent to $\mu (p − 1) \pmod {p}$ in Article 81. I read it, but is there a faster proof …

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 …

Proof of existence of primitive roots Ask Question Asked 11 years, 6 months ago Modified 11 years, 6 months ago