Hello,

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 :

and

So

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.