Question 3 Let n be an integer with n 2 For all a b and c in

Question 3:

Let n be an integer with n 2. For all a; b and c in Z, is it true that [ [a + b]_n + c]_n = [a + [b + c]_n]_n ?

Justify your answer.

Note : the subject is abstract algebra charles c.printer

Solution

solution

given

[[a+b]n+c]n= [a+[b+c]n]n

[[a+b]n+c]n= [a+[b+c]n]n

[an+bn+c]n= [an+[b+c]n²]

an²+bn²+cn=an+bn²+cn²

an²+cn=an+cn²

an-a=cn-c

a(n-1)=c(n-1)

a=c

now put a=c in equation

[[c+b]n+c]n= [c+[b+c]n]n

so we can say

LHS=RHS