determine the greatest possible number of elements of a subset A of {1,2,.....,30} with the property that any product of one or more distinct elements of A is not a square.

Question

anonymous · Answer

how many elements,i think the question is asking

anonymous · Answer

how any numbers in the set , are not squares when multiplied

anonymous · Answer

actually this question do they also mean we can also multiply the number by its self or we muldiply different numbers to check if their product is a squre?

anonymous · Answer

can we say all primes are never perfect squares when multiplied by a natural number,
ie <30
$$p \times n=c^2$$
eg 3(n)=perfect square

anonymous · Answer

yes

anonymous · Answer

oh yah but it has to be multiplied by its cube,so how d we eliminate non squares