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???