If then for some .

This means, .

Since by Euler's theorem.

Consider the group .b) Prove that for any integer, n

n^11 is congruent to n mod 33.

This group is isomorphic to .

Therefore, has exponent i.e. it means .

Thus, if it would mean so .

Now if then it means .

If there is nothing to prove.

To complete the proof note that if this is true by mods.

Thus, if for example then with relatively prime to .

But then .

And with that this completes the proof.