check whether (p+1)is a factor of p^100-1and p^101-1
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Let p−1=0
p=1
For p−1 to be factor, the equation on substituting p=1 should equate to 0
i) f(p)=p
10
−1
f(1)=1−1=0
ii) f(p)=p
11
−1
f(1)=1−1=0
∴ Hence p−1 is a factor of both
p
10
−1 & p
11
−1
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