Answer:
If  is divisible by 3, the n is also divisible by 3.
 is divisible by 3, the n is also divisible by 3.
Step-by-step explanation:
We will prove this with the help of contrapositive that is we prove that if n is not divisible by 3, then,  is not divisible by 3.
 is not divisible by 3.
Let n not be divisible by 3. Then  can be written in the form of fraction
 can be written in the form of fraction  , where x and y are co-prime to each other or in other words the fraction is in lowest form.
, where x and y are co-prime to each other or in other words the fraction is in lowest form.
Now, squaring

Thus, 


It can be clearly seen that the fraction  is in lowest form.
 is in lowest form.
Hence,  is not divisible by 3.
 is not divisible by 3.
Thus, by contrapositivity if  is divisible by 3, the n is also divisible by 3.
 is divisible by 3, the n is also divisible by 3.