Problem E: Perfect Pth Powers
We say that x is a perfect square if, for some integer b,
x = b2. Similarly, x is a perfect cube if, for some integer
b, x = b3. More generally, x is a perfect pth
power if, for some integer b, x = bp. Given an
integer x you are to determine the largest p such that x
is a perfect pth power.
Each test case is given by a line of input containing x.
The value of x will have magnitude at least 2 and be within the
range of a (32-bit) int in
C, C++, and Java. A line containing 0 follows the last test case.
For each test case, output a line giving the largest integer p such that x is
a perfect pth power.
Output for Sample Input
G. V. Cormack