સાબિત કરો :  $p-1$ એ $p^{10}-1$ અને $p^{11}-1$ નો એક અવયવ છે. 

If $p-1$ is a factor of $p^{10}-1,$ then $(1)^{10}-1$ should be equal to zero.

Now, $(1)^{10}-1=1-1=0$

Therefore, $p-1$ is a factor of $p^{10}-1.$

Again, if $p -1$ is a factor of $p^{11}-1,$ then $(1)^{11}-1$ should be equal to zero. Now, $(1)^{11}-1=1-1=0.$

Therefore, $p -1$ is a factor of $p^{11}-1.$

Hence, $p -1$ is a factor of $p^{10}-1$ and also of $p^{11}-1.$