2010/032) If p and q are distinct primes, show that p^q + q^p ≅ (p + q) mod pq

If p and q are distinct primes, show that p^q + q^p ≅ (p + q) mod pq.
as

q is prime

so p^(q-1) mod q = 1 (as per fermats little theorem)


so p^(q-1) = mq + 1

multiply by p on both sides p^q = mpq + p = p mod pq

similarly as q is prime q^p = p mod pq

adding we get (p^q + q^p) mod pq = (p+q)

proved