Editing Computational number theory (section)

{{short description|Study of algorithms for performing number theoretic computations}}
In [[mathematics]] and [[computer science]], '''computational number theory''', also known as '''algorithmic number theory''', is the study of 
[[computation|computational methods]] for investigating and solving problems in [[number theory]] and [[arithmetic geometry]], including algorithms for [[primality testing]] and [[integer factorization]], finding solutions to [[diophantine equations]], and explicit methods in [[arithmetic geometry]].{{r|pcm}}
Computational number theory has applications to [[cryptography]], including [[RSA (cryptosystem)|RSA]], [[elliptic curve cryptography]] and [[post-quantum cryptography]], and is used to investigate [[conjectures]] and [[open problems]] in number theory, including the [[Riemann hypothesis]], the [[Birch and Swinnerton-Dyer conjecture]], the [[ABC conjecture]], the [[Modularity theorem|modularity conjecture]], the [[Sato-Tate conjecture]], and explicit aspects of the [[Langlands program]].{{r|pcm}}{{r|bachshallit}}{{r|cohen}}