I am stuck on a cryptography problem that pertains to Elliptic Curves.
The problem is stated as follows:
Assume the cubic polynomial $X^3+AX+B = (X-a)(X-b)(X-c)$
If $4A^3 + 27B^2 = 0$, then show two or all of $a,b,c$ are the same.
So far, I expanded the right side, so I get the following equations:
$0 = a + b + c$
$A = ab + ac + bc$
$B = -abc$
I can't seem to use the hypothesis in the correct way. I tried to compute $A^3$ but the expansion of it looks horrible. If any one has any tips how to approach this problem, that would be great.