A perfect square is defined as the square of an integer and a perfect cube is defined as the cube of an integer. How many positive integers n are there such that n is less than 100,000 and at the same time n is a perfect square and a perfect cube?
Choose one.
A) 3  B) 4  C) 5  D) 6  E) 7
If n is a perfect square and a perfect cube, then n = a^6 for some integer a.   The numbers are 1^6=1, 2^6=64, 3^6= 729, 4^6=4096, 5^6=15,625, 6^=46,656.   The answer is 6.
<result>D</result>
A perfect square is defined as the square of an integer and a perfect cube is defined as the cube of an integer. How many positive integers n are there such that n is less than 100,000 and at the same time n is a perfect square and a perfect cube?