Problem 42829. Number construction III

Given a positive integer, n, return a, b and c, such that

1. n = a^1.5+b^2.5+c^3.5

2. a, b and c are all positive integers greater than 1

If a solution does not exist, set all three output variables to zero.

Example 1:

n = 168

a = 4

b = 4

c = 4

Example 2:

n = 100

a = 0

b = 0

c = 0