Properties of numbers : Number Theory #Properties #of #numbers : #Number #Theory
So far we have seen about the historical background to Number Theory. Now we enter into subject starting with the basic definitions & properties of Numbers. Contents : * The Principle of Induction * The well - Ordering Principle * Divisibility * Properties of Divisibility * Greatest Common Divisor (gcd) * properties of gcd The Principle of Induction : If Z is the set of all integers such that i) 1 𝜖 Z ii) n 𝜖 Z implies n+1 𝜖 Z then iii) all integers ≥ 1 belong to Z. In another manner The principle of induction is useful to define a statement p(n) is exists for all integers n which are to be proved in the following steps. i) We have to prove P(1) is true i.e. the statement is true for n=1 ii) Assume P(k) is true i.e. the statement is true for n=k iii) Again we have to pro...