How to prove this property of modulo arithmetic?

[colerelm]

How could I prove (a+b) mod n = [(a mod n) + (b mod n)] mod n?

 

[daon2]

What have you tried? Let me restate it for you: Let r,s,t be the remainders when a,b,(a+b) are divided by n respectively. Then the remainder when r+s is divided by n is equal to t.

 

[HallsofIvy]

If x= a+ b (mod n) then x= kn+ a+ b for some integer k. Choose any integer i and define j= k- i then k= i+ j so x= kn+ a+ b= (i+ j)n+ a+ b= in+ jn+ a+ b= (in+ a)+ (jn+ b)