Show that, if n 2 and if p is a prime which divides n but is such that p is not a factor of n, then p(n)+1 = p mod n. Can you find and prove a generalisation of this? [Hint for first part: n may be written as pm, and (p, m) = 1; consider powers of p modulo m. Hint for second part: for example, you may check that, although 29(100)+1 is not congruent to 2 mod 100, one does have 2(100)+2 congruent to 2 mod 100; also 620+1 = 6 mod 66.]