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Question
Show that p – 1 is a factor of p10 – 1 and also of p11 – 1.
Solution
Let g(p) = p10 – 1 ...(i)
And h(p) = p11 – 1 ...(ii)
On putting p = 1 in equation (i), we get
g(1) = 110 – 1
= 1 – 1
= 0
Hence, p – 1 is a factor of g(p).
Again, putting p = 1 in equation (ii), we get
h(1) = (1)11 – 1
= 1 – 1
= 0
Hence, p – 1 is a factor of h(p).
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