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