I was thinking over the following problem. Let be any composite number divisible by . Let :
for and .
So, . Furthermore, an additional property is required, which is that , .
Finally, the last property is that when the polynomial is factorized into , neither of the factors equal when .
I got to the before-last part, because I noticed that :
But each time I apply this formula to find , and , it turns out that the factorized form of the polynomial yields a factor equal to when . Why is that ? Why doesn't it yield a nontrivial factor of ? Does it come from the formula ?
This might not be very clear ... If you need me to make it clearer don't hesitate. Thanks all.