A bit less than perfect


For all numbers \(x\), \[x^{2}-1=(x+1)\times(x-1)\]

Five collegiate math students are discussing this subject:

Alice: "Since \(x^{2}-1\) 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 \(x^{2}-1\), where \(x\) is any number, is \(-1\)."

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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