A Cubic number and A Cubic Number HDU - 6216 （数学）

A cubic number is the result of using a whole number in a multiplication three times. For example, 3×3×3=27so 27 is a cubic number. The first few cubic numbers are 1,8,27,64 and 125. Given an prime number pp. Check that if pp is a difference of two cubic numbers.
Input
The first of input contains an integer T (1≤T≤100) which is the total number of test cases.
For each test case, a line contains a prime number $p(2≤p≤10^{12})$.
Output
For each test case, output ‘YES’ if given pp is a difference of two cubic numbers, or ‘NO’ if not.
Sample Input
10
2
3
5
7
11
13
17
19
23
29
Sample Output
NO
NO
NO
YES
NO
NO
NO
YES
NO
NO
问题是给定素数$p$，是否存在$a、b$使得满足等式：

$$p=a^3-b^3(a>b)$$ 若存在输出YES，没有则NO
这个算数学题了吧，或是数论，这种题在acm已经是水题了。。。
易知： $$p=(a-b)(a^2+ab+b^2)$$
因为p为素数，所以$a-b=1$，则：
$$p=(b+1)^3-b^3=3b^2+3b+1$$
转化为 $$3b^2+3b+1-p=0$$
是否有整数解的问题，这个就很显然了，只要验证$9+12（p-1）是否是一个平方数$

代码就没必要写了