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 …

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 $13$. $ (*)$

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

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

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 …

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 …

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 …

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

The proof of the primitive element theorem may yield the primitive element $\sqrt 2 +\sqrt 3+\sqrt 5$, depending on how it's proved.

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