factoring the difference of squares

Question

q to the second power + 1

 

is it a prime

Answer 1

Hi Dawn,

Without more information about "q", q² + 1 can be either prime or not prime.  By example, if q=5, the q²+1=25+1=26 which is not prime AND if q=6, then q²+1=36+1=37 which is prime.

Even q²-1 can be prime if q=2 since 2²-1=3 which is prime!

Was there more information about q in the original question?

Answer 2

q²+1 is prime

q²-1 is not prime and it is the difference of two squares

q²-1=(q+1)(q-1)