What is a good introductory textbook for Number Theory at the university level?

In summary, the individual is seeking recommendations for a Number Theory book that is taught in university, without including introductory concepts or advanced proofs. They have completed an A-Level in Maths and are interested in learning more about Number Theory. They have been advised to look into the Open University and to read a specific thread on the Physics Forums website.
  • #1
tomfitzyuk
15
0
Hey,

I'm interested in Number Theory and have seen a few simple proofs/concepts related to Number Theory but at moment I have no other reference.

Could somebody recommend me a Number Theory which will teach it as it's taught when you start university.

I've done an A-Level in Maths in case you're wondering my level of education. So I don't want a book with the proof of Fermat's Last Theorem in the introductory chapter nor do I want an introduction to counting.

Thanks in Advance
Tom
 
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  • #3
the british ou-university ,try to get in touch with the ou.
 

What is number theory?

Number theory is a branch of mathematics that deals with the properties and relationships of integers. It involves studying patterns, relationships, and properties of numbers and how they can be manipulated and applied in various mathematical contexts.

What are prime numbers?

Prime numbers are numbers that are only divisible by 1 and itself. Examples of prime numbers include 2, 3, 5, 7, 11, and so on. The study of prime numbers is an important part of number theory, as they have many intriguing properties and applications in mathematics and computer science.

What is the fundamental theorem of arithmetic?

The fundamental theorem of arithmetic states that every positive integer can be expressed as a unique product of prime numbers. This theorem is the basis for many other important theorems and concepts in number theory, such as the Euclidean algorithm and the concept of greatest common divisor.

What is the difference between rational and irrational numbers?

Rational numbers are numbers that can be expressed as a fraction, where the numerator and denominator are integers. Irrational numbers, on the other hand, cannot be expressed as a fraction and have non-terminating and non-repeating decimal expansions. Examples of irrational numbers include pi and the square root of 2.

How is number theory used in cryptography?

Number theory plays a crucial role in cryptography, which is the study and practice of secure communication. Prime numbers, modular arithmetic, and other concepts from number theory are used in cryptographic algorithms to ensure the security of data transmission and storage.

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