Question

Show that p-1 is a factor of p^10-1 and also of p^11-1​

Answer 1

Answer:

Step-by-step explanation:

Well, this question here may be a little bit difficult to make you understand out here as we only have access to MS word doc. A lot of other functions needs to be accessed so white board or a chalk board is the best option, still will try my best.

You asked to prove that (p^-1) is a factor of both p^10-1 and p^11-1

Lets see,

Assuming here that  g(p) = p^10-1.

  H(p) = p^11-1, we try and plug in values for p -1 in equation g(p) = p^10-1, we get

  g(1) = 1^10-1 = 1 – 1 (as 1^10 = 1)

  g(1) = 1-1 = 0. So, p-1 is a factor of g(p).

Now again, we plug in p = 1 in second equation, and we get

  h(1) = (1) 11-1 = (1)^10-1 = 1-1 = 0. Hence p-1 is a factor of h(p).

I HOPE IT HELP YOU