# Are there any resources for questions on primitive roots?

• matqkks
In summary, primitive roots are the smallest numbers that can generate all the values in a given set of numbers when raised to certain powers. There are multiple methods for finding primitive roots, including trial and error, the primitive root theorem, and modular arithmetic. They have various applications in number theory, cryptography, and computer science, making them useful for mathematical and scientific research. Resources such as textbooks, online courses, and academic papers are available for learning more about primitive roots. It is recommended to consult with a professor in mathematics or computer science for guidance on which resources would be most beneficial for one's specific interests and needs.
matqkks
Does anyone know of any resources on questions on primitive roots and order of a modulo n? They need to be suitable for elementary number theory course. (These could be interesting results and challenging ones).

Perhaps @fresh_42 can suggest some examples.

I think I already did in a previous thread: encryptions, error correcting codes, DFFT, prime tests, or any basic algebra textbook. I don't remember details or a certain book, other than standard materials. The question is also very unspecific.

jedishrfu

## 1. What are primitive roots?

Primitive roots are numbers that, when raised to certain powers, can generate all the values in a given set of numbers. In other words, they are the smallest numbers that can create all the possible values in a given set.

## 2. How do I find primitive roots?

There are several methods for finding primitive roots, including trial and error, using the primitive root theorem, and using modular arithmetic. It is recommended to consult a math textbook or online resources for specific instructions on how to find primitive roots.

## 3. What are the applications of primitive roots?

Primitive roots have various applications in number theory, cryptography, and computer science. They are used in encryption algorithms, prime number generation, and generating random numbers.

## 4. Can I use primitive roots in my research?

Yes, primitive roots can be used in mathematical and scientific research, particularly in the fields of number theory and cryptography. However, it is important to have a strong understanding of their properties and applications before incorporating them into your research.

## 5. Are there any resources for learning more about primitive roots?

Yes, there are many resources available for learning more about primitive roots, including textbooks, online courses, and academic papers. It is recommended to consult with a mathematics or computer science professor for guidance on which resources would be most helpful for your specific interests and needs.

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