A bit less than perfect


For all numbers zz, z21=(z+1)×(z1)z^{2}-1=(z+1)\times(z-1)

Five math students are discussing this subject:

Alice: "Since z21z^{2}-1 is a product of 2 numbers, all positive integers 1 less than a perfect square are composite."

Ben: "All integers 1 more than a perfect square are prime."

Charlie: "The lowest possible value for z21z^{2}-1, where zz is any number, is 1-1."

Drake: "None of you are correct."

Emily: "To build off of what Drake said, all of you are wrong because the equation itself is wrong."

Which student is correct?

For clarity: When the term, "number," is stated, it means any number that can be found in the complex plane.


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