A complete residue system modulo m is a set of integers such that every integer is congruent modulo m to exactly one integer of the set. If a1,a2,...,am is a complete residue system mo...A complete residue system modulo m is a set of integers such that every integer is congruent modulo m to exactly one integer of the set. If a1,a2,...,am is a complete residue system modulo m, and if k is a positive integer with (k,m)=1, then ka1+b,ka2+b,...,kam+b is another complete residue system modulo m for any integer b.
The Euler ϕ-function is the map ϕ:N→N defined by ϕ(n)=1 for n=1, and, for n>1,ϕ(n) is the number of positive...The Euler ϕ-function is the map ϕ:N→N defined by ϕ(n)=1 for n=1, and, for n>1,ϕ(n) is the number of positive integers m with 1≤m<n and gcd
We now present several multiplicative number theoretic functions which will play a crucial role in many number theoretic results. We start by discussing the Euler phi-function which was defined in an ...We now present several multiplicative number theoretic functions which will play a crucial role in many number theoretic results. We start by discussing the Euler phi-function which was defined in an earlier chapter. We then define the sum-of-divisors function and the number-of-divisors function along with their properties.
