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:

• Prime numbers
• Factorization
• Matrix

Important theorems in number theory are:

• Chinese remainder theorem
• Fundamental theorem of arithmetic
• Fermat's last theorem
• Fermat's little theorem

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

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  The Babylonians demonstrated an early understanding of Pythagorean triples.

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  The Riemann hypothesis is of interest in analytic number theory.

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  Number theorists Paul Erdős and Terence Tao in 1985, when Erdős was 72 and Tao was 10

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  Riemann zeta function ζ(s) in the complex plane. The color of a point s gives the value of ζ(s): dark colors denote values close to zero and hue gives the value's argument.

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  The action of the modular group on the upper half plane. The region in grey is the standard fundamental domain.

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  Corrections to an estimate of the prime-counting function using zeros of the zeta function

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  Two examples of elliptic curves, that is, curves of genus 1 having at least one rational point

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  A Lehmer sieve, a primitive digital computer used to find primes and solve simple Diophantine equations

Other websites

• Media related to Number theory at Wikimedia Commons
• Number Theory Archived 2023-10-30 at the Wayback Machine
• Number Theory Web