State Fermat's Theorem and Wilson's Theorem.
For which prime numbers does the equation have a solution? Justify your answer.
For a prime number , and an integer that is not a multiple of , the order of is the least positive integer such that . Show that if has order and also then must divide .
For a positive integer , let . If is a prime factor of , determine the order of . Hence show that the are pairwise coprime.
Show that if is a prime of the form then cannot be a factor of any . Give, with justification, a prime of the form such that is not a factor of any .