theleastnumberof numberstobedeletedfromtheset{1,2,3.,13,14,15}sotheproductoftheremainingnumbersisperfectsquare

Question

a)1
b)2
c)3
d)4

Answer 1

"The least number of numbers to be deleted from the set {1, 2, 3, ..., 14, 15} so the product is a perfect square."

Let's first investigate the prime content of the product 1 * 2 * ... * 14 * 15 = 15!

It is 2^11 * 3^6 * 5^3 * 7^2 * 11 * 13

We must make all exponents even, so we need to get rid of one factor of each of
2, 5, 11 and 13.

This is accomplished by removing 10, 11 and 13. Therefore, you need to delete three numbers.