Prove: if n is a positive integer andn2 is
divisible by 3, then n is divisible by3.

Answer and Step-by-step explanation:

n > 0

n² divisible by 3 ⇒ n is divisible by 3.

Any number divisible by 3 has the sum of their components divisible by 3.

If n² is divisible by 3,  we can say that n² can be written as 3*x.

n² = 3x ⇒ n = √3x

As n is a positive integer √3x must be a integer and x has to have a 3 factor. (x = 3.a.b.c...)

This way, we can say that x = 3y and y is a exact root, because n is a integer.

n² = 3x ⇒ n = √3x ⇒ n = √3.3y ⇒ n = √3.3y ⇒ n = √3²y ⇒ n = 3√y

Which means that n is divisible by 3.