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 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.

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  w:Plimpton 322, Babylonian tablet listing pythagorean triples

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  Title page of the 1621 edition of Diophantus of Alexandria's Arithmetica, translated into Latin by Claude Gaspard Bachet de Méziriac

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  Al-Haytham as seen by the West: on the frontispiece of Selenographia Alhasen [sic] represents knowledge through reason and Galileo knowledge through the senses.

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  PierredeFermat

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  LeonhardEuler

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  "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.

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  Carl Friedrich Gauss's Disquisitiones Arithmeticae, first edition

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  Portrait of the mathematician and philosopher Carl Friedrich Gauss

Other websites

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