A positive integer is called "square-Free" if it has no factor that is the square of an integer greater than 1. If n is an even square-free integer, which of the following must also be square free? Choose the most appropriate option:	A) n/2	B) 2n	C) n+2	D) n^2	E) none of the above
Per definition a square-free integer has primes in power of 1. For example 5^3 is NOT square-free because it's a multiple of 5^2.   We are told that n=2k, since n itself is square-free, then k also must be square-free --&gt; n/2=k.   Answer: A.   number for n. Say n=2, then among n/2, B, C, and D, only n/2 (n/2=1) will be square free.
<result>A</result>
A positive integer is called "square-Free" if it has no factor that is the square of an integer greater than 1. If n is an even square-free integer, which of the following must also be square free?