Question

prove that p-1 divides p^10-1 and p^11 ​-1

Answer 1

Step-by-step explanation:

Let g (p) = p10 -1

and h(p) = p11 -1.

On putting p=1 in Eq. (i), we get

g(1)=110-1= 1-1=0 Hence, p-1 is a factor of g(p).

Again, putting p = 1 in Eq. (ii), we get

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