Bunuel wrote:

shrive555 wrote:

Is positive integer n is divisible by 4 ?

1) n^2 is divisible by 8

2) sqr/n is even integer.

any good explanation please

(1) n^2 is divisible by 8 --> \(n^2=8p=2^3*p\) --> in order n^2 to be a perfect square p must complete the power of 2 to even number (perfect square has even powers of its prime factors) --> \(n^2=8p=2^3*2q=2^4q\) --> \(n=\sqrt{2^4q}=4\sqrt{q}\). Sufficient.

(2) \(\sqrt{n}=2k\) --> \(n=4k^2\). Sufficient.

Answer: D.

Bunuel, what made you think about :

in order n^2 to be a perfect square p must complete the power of 2 to even number (perfect square has even powers of its prime factors)

why n^2 be a perfect square???