Primitive Vs Non Primitive

In recent times, primitive vs non primitive has become increasingly relevant in various contexts. calculus - Why is "antiderivative" also known as "primitive .... 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 here How common is the use of the term "primitive" to mean "antiderivative"?, some languages such as Dutch only use the term, primitive. Are all natural numbers (except 1 and 2) part of at least one primitive .... Hence, all odd numbers are included in at least one primitive triplet.

Except 1, because I'm not allowing 0 to be a term in a triplet. I can't think of any primitive triplets that have an even number as the hypotenuse, but I haven't been able to prove that none exist. Finding a primitive root of a prime number. In this context, how would you find a primitive root of a prime number such as 761? How do you pick the primitive roots to test?

What are primitive roots modulo n? - Mathematics Stack Exchange. You'll need to complete a few actions and gain 15 reputation points before being able to upvote. Upvoting indicates when questions and answers are useful.

What's reputation and how do I get it? In this context, instead, you can save this post to reference later. In this context, elementary number theory - Find all the primitive roots of $13 .... Primes have not just one primitive root, but many. So you find the first primitive root by taking any number, calculating its powers until the result is 1, and if p = 13 you must have 12 different powers until the result is 1 to have a primitive root.

Show that $2$ is a primitive root modulo $13$.. I thought $\varphi (12)$ counts the number of coprimes to $12$.. Why does this now suddenly tell us the number of primitive roots modulo $13$?

How have these powers been plucked out of thin air? I understand even powers can't be primitive roots, also we have shown $2^3$ can't be a primitive root above but what about $2^9$? This perspective suggests that, what is a primitive root?

I have read that, but essentially what I want to know is, can a primitive root be defined in a simpler, easier to understand way? For my level of mathematics, some of the more formal definitions can be hard to understand sometimes Moreover, logic - To what extent can Primitive Recursion perform wellfounded .... In fact, primitive recursive functions can perform a huge variety of set-theoretic tasks, which makes primitive wellfounded recursion straightforward... Or at least, it's straightforward to anyone who's familiar with the ordinary proofs of wellfounded recursion.