Giuga's conjecture says that this equation is also a sufficient condition for p to be prime. Another consequence of Fermat's little theorem is the following: if p is a prime number other than 2 and 5, 1/p is always a recurring decimal, whose period is p − 1 or a divisor of p − 1. The fraction 1/p expressed likewise in base q (rather than base 10) has similar effect, provided that p is not a prime factor of q. Wilson's theorem says that an integer p > 1 is prime if and only if the factorial (p − 1)! + 1 is divisible by p. Moreover, an integer n > 4 is composite if and only if (n − 1)! is divisible by n.
Assuming p is a prime other than 2 or 5, then, according to Fermat's theorem, what type of decimal will 1/p always be? According to Fermat's theorem, what period does 1/p always have assuming p is prime that is not 2 or 5? According to Wilson's theorem, what factorial must be divisible by p if some integer p > 1 is to be considered prime? According to Wilson's theorem, what factorial must be divisible by n if some integer n > 4 is to be considered composite? What condition what must be satisfied in order for 1/p to be expressed in base q instead of base 10 and still have a period of p - 1?