How the product of all divisors is n^(x)?

#1

I was solving the problem of “Playing with Divisors is Fun”.

In the solution, it is given that, the product of all divisors of n is n^(x) where x = no. of divisors.

But, if n = 30, x = 8. In this example, the product of divisors is 30^4 = 810000 and not 30^(8).

I am not able to understand this concept.

#2

It’s written incorrectly , its actually n^(x/2).
In the code it is considered to be x/2, see this line

vec[i] = (vec[i]*500000004)%p; // 500000004 is mod_inv(2,1000000007);

It is multiplied by multiplicative inverse of 2.

#3

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