Hence we know that
For to be equal to 17, 17 must be equal to one of the factors, let's say , because 17=17*1 is the only factorisation for 17.
So it means that the others factors are equal to 1, that is to say . Thus since all the other powers are 0. (this is an extra part lol)
Let's go back to the problem.
This can be factorised :
But the only prime number that divides 16 is 2. Therefore .
Thus , which is impossible because the left hand side is an odd number and the right hand side is an even number.