Thread: Factor Theorem Troubles

Hey Guys, I have two problems that have to do with the factor theorem. I've been stumped on them for sometime now and can no longer put them off as my assignment is due soon.

1) Use the factor theorem to show that if 2^p - 1, where p does not equal 3, is a prime number, then p is neither divisible by 4 or divisible by 3. {Alternatively, prove that if p is divisible by 4 or 3, the 2^p - 1 is divisible by some number other than +/- itself or +/-1.}

Known, factor theorem: p(x) = q(x)(x-a) +r(x)

I've tried setting 2^p - 1 = 0, but I get P log 2 = 0, I guess if someone could give me a hint or push me in the right direction I'd greatly appreciate it. thanks

Hello cndman

Originally Posted by cndman

Hey Guys, I have two problems that have to do with the factor theorem. I've been stumped on them for sometime now and can no longer put them off as my assignment is due soon.

1) Use the factor theorem to show that if 2^p - 1, where p does not equal 3, is a prime number, then p is neither divisible by 4 or divisible by 3. {Alternatively, prove that if p is divisible by 4 or 3, the 2^p - 1 is divisible by some number other than +/- itself or +/-1.}

Known, factor theorem: p(x) = q(x)(x-a) +r(x)

I've tried setting 2^p - 1 = 0, but I get P log 2 = 0, I guess if someone could give me a hint or push me in the right direction I'd greatly appreciate it. thanks

We use two results here:

and

First, suppose that . Then

has a factor and a factor .

Now suppose that . Then

has a factor and a factor

Grandad