Show that if 3 divides n2 evenly then 3 divides n evenly. [Hint: n can only be of the form 3a, 3a + 1 or 3a +?

Question

thats meant to say n^2

Answer 1

Taking from where u left,
the squares can only be of the forms
(3a)^2 = 9a^2,
or
(3a+1)^2 = 9a^2 + 6a + 1,
or
(3a+2)^2 = 9a^2 + 12a + 4

The last two will leave a remainder 1, thus the square is divisible by 3 only if the number is.

Answer 2

If 3 divides n^2 n^2 contains the prime factor 3
But n and n^2 have the same prime factors only that those of n^2 have double exponent.So if n`2 contains prime factor 3 n also contains it because if not 3 would no be factor of n^2
ex. n= 2^3 *3^5 n^2 = 2 ^6*3^10