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Class 9-10, JEE & NEET
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Show that p-1 is a factor of p10 -1 and also of p11 -1.
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).