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Reference.org
Computational number theory
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<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a> and <a href="/facts/Computer_science/lN3pEyPz">computer science</a>, computational number theory, also known as algorithmic number theory, is the study of <a href="/facts/Computation/qLsELosq">computational methods</a> for investigating and solving problems in <a href="/facts/Number_theory/zhoa7zrc">number theory</a> and <a href="/facts/Arithmetic_geometry/Bs1mfNu4">arithmetic geometry</a>, including algorithms for <a href="/facts/Primality_testing/dLMr8E0u">primality testing</a> and <a href="/facts/Integer_factorization/EjMCTz2t">integer factorization</a>, finding solutions to <a href="/facts/Diophantine_equations/mYaHp7oX">diophantine equations</a>, and explicit methods in <a href="/facts/Arithmetic_geometry/Bs1mfNu4">arithmetic geometry</a>. Computational number theory has applications to <a href="/facts/Cryptography/e94PEVau">cryptography</a>, including <a href="/facts/RSA_(cryptosystem)/XTzyfHuq">RSA</a>, <a href="/facts/Elliptic_curve_cryptography/YbjcXIWk">elliptic curve cryptography</a> and <a href="/facts/Post-quantum_cryptography/1qeqUQve">post-quantum cryptography</a>, and is used to investigate <a href="/facts/Conjectures/oPWUb7SF">conjectures</a> and <a href="/facts/Open_problems/VuR6yLsW">open problems</a> in number theory, including the <a href="/facts/Riemann_hypothesis/Td8Jq5r0">Riemann hypothesis</a>, the <a href="/facts/Birch_and_Swinnerton-Dyer_conjecture/Issh7Yfr">Birch and Swinnerton-Dyer conjecture</a>, the <a href="/facts/ABC_conjecture/yJeHld4Q">ABC conjecture</a>, the <a href="/facts/Modularity_theorem/aI3HRxwj">modularity conjecture</a>, the <a href="/facts/Sato-Tate_conjecture/BK5wTDyU">Sato-Tate conjecture</a>, and explicit aspects of the <a href="/facts/Langlands_program/koK9PhID">Langlands program</a>. </p>