Number theory is one of branches of mathematics which deals with relations between Integer Numbers (positive and negative natural numbers and zero) which shown as Z numbers.<\/p>\n\n\n\n
Number theory, as a course in undergraduate of mathematics, usually starts with topic of \u201cDivisibility\u201d. This section involves with some sub-topics like \u201cdivision algorithm\u201d, \u201cGreatest Common Divisor\u201d, \u201cLeast Common Multiple\u201d, \u201cEuclid Algorithm\u201d, \u201cPrime Numbers\u201d, \u201cSieve of Eratosthenes\u201d, \u201cFundamental Theorem of Arithmetic\u201d, \u201cLinear Diophantine Equations\u201d and etc.<\/p>\n\n\n\n\n\n\n\n
There are some famous theorems and conjectures related to this section which are: \u201cChebyshev’s Theorem\u201d, \u201cDirichlet’s Theorem\u201d, \u201cBertrand’s conjecture\u201d and \u201cGoldbach’s conjecture\u201d.<\/p>\n\n\n\n
Another section of this course is \u201cModular Arithmetic\u201d which is in concept is like \u201cDivisibility\u201d but it has its own terminology and its own theorems to solve number theory problems. This section involves with some sub-topics like: \u201cResidue Numeral System (RNS)\u201d, \u201cModular Equations System\u201d, \u201cPrimitive Root Modulo of n\u201d, \u201cChinese Reminder Theorem\u201d and etc.<\/p>\n\n\n\n
There are some theorems in this section too which the most famous one that usually taught in universities are: \u201cFermat’s little theorem\u201d, \u201cHensel’s Lemma\u201d, \u201cEuler’s Totient Function\u201d, \u201cEuler’s Theorem\u201d and \u201cWilson’s Theorem\u201d.<\/p>\n\n\n\n
In summary, \u201cNumber Theory\u201d is almost a branch of \u201cPure Mathematics\u201d which means, all of the theorems and applications only involves in mathematics and there is no application of it in other sciences or in a real world scenario. Although, there are some applications of \u201cNumber Theory\u201d in \u201cCryptography\u201d and Encryption \/ Decryption methods and maybe by growing other fields like this, we observe more application of number theory in other sciences. It is also worth mentioning that this field of Mathematics and its problems are very hard to study and as you will see when involving with this field, there are many unsolved problems and conjectures in \u201cNumber Theory\u201d.<\/p>\n","protected":false},"excerpt":{"rendered":"
Number theory is one of branches of mathematics which deals with relations between Integer Numbers (positive and negative natural numbers and zero) which shown as Z numbers. Number theory, as a course in undergraduate of mathematics, usually starts with topic of \u201cDivisibility\u201d. This section involves with some sub-topics like \u201cdivision algorithm\u201d, \u201cGreatest Common Divisor\u201d, \u201cLeast […]<\/p>\n","protected":false},"author":1,"featured_media":521,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_post_was_ever_published":false},"categories":[102,123],"tags":[124,125,122],"class_list":["post-511","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mathematics","category-number-theory","tag-mathematics","tag-modular-arithmetic","tag-number-theory"],"yoast_head":"\n