# Number theory

**Number theory** is a part of mathematics. It explains what some types of numbers are, what properties they have, and ways that they can be useful.

Topics in number theory are:

Important theorems in number theory are:

## Applications

A well-known application of number theory is encrypted messaging (encryption). Data compression also makes use of the field.

## Further reading

- G.H. Hardy; E.M. Wright (2008) [1938]. An introduction to the theory of numbers. Oxford University Press. ISBN 978-0-19-921986-5.
- Vinogradov, I.M. (2003) [1954]. Elements of Number Theory (reprint o 1954 ed.). Mineola, NY: Dover Publications.
- Ivan M. Niven; Herbert S. Zuckerman; Hugh L. Montgomery (2008) [1960]. An introduction to the theory of numbers (reprint of the 5th edition 1991 ed.). John Wiley & Sons. ISBN 978-81-265-1811-1.
- Kenneth H. Rosen (2010). Elementary Number Theory (6th ed.). Pearson Education. ISBN 978-0-321-71775-7.
- Borevich, A. I.; Shafarevich, Igor R. (1966). Number theory. Pure and Applied Mathematics. 20. Boston, MA: Academic Press. ISBN 978-0-12-117850-5. MR 0195803.
- Serre, Jean-Pierre (1996) [1973]. A course in arithmetic. Graduate texts in mathematics. 7. Springer. ISBN 978-0-387-90040-7.

## Number Theory Media

The distribution of prime numbers is a central point of study in number theory. This Ulam spiral serves to illustrate it, hinting, in particular, at the conditional independence between being prime and being a value of certain quadratic polynomials.

Title page of the 1621 edition of Diophantus of Alexandria's

*Arithmetica*, translated into Latin by Claude Gaspard Bachet de MéziriacAl-Haytham as seen by the West: on the frontispiece of

*Selenographia*Alhasen [*sic*] represents knowledge through reason and Galileo knowledge through the senses."Here was a problem, that I, a ten-year-old, could understand, and I knew from that moment that I would never let it go. I had to solve it." —Sir Andrew Wiles about his proof of Fermat's Last Theorem.

## Other websites

- Media related to Number theory at Wikimedia Commons
- Number Theory
- Number Theory Web