Mod question

1. The problem statement, all variables and given/known data
if n is congruent to 6 mod 5
then n is congruent to 1 mod 5?

2. Relevant equations


3. The attempt at a solution

This is not a problem. It's a doubt that I have

 

x is a number between 0 and 5

 

5 divides n-x

 

I got it by algebra 5 divides n-6 so n-6=5k, n=5(k+1)+1, so 5 divides n-1 which implies n is congruent to 1 mod 5. I am having another inquiry with my friend. He claims that 16 is not congruent to 2 mod 7 because he thinks that a^2 congruent to b mod n implies that b has to be a perfect square. Is that correct?