Question

Let S be the number of perfect squares among the integers from 1 to 20136. Let Q be the number of perfect cubes among the same integers. What is the relationship between S and Q?

Answer 1

4 9 16 25 * 36 49 64 81 100 121 * 144 169
8 ********27******64 ********* 125 *****

Oh well, I can say that Q < S :)

Answer 2

4 9 16 25 * 36 49 64 81 100 121 * 144 169 196 * 225
8 ********27******64 ********* 125 ********216

Answer 3

2013^6 is the perfect square of 2013^3 meaning that S = 2013^3
2013^6 is the perfect cube of 2013^2 meaning that Q = 2013^2
Therefore 2013Q = S