2011/033) Prove: If p and q are distinct primes, show that p^q + q^p ≅ (p + q) mod pq

q is prime

so p^(q-1) mod q = 1 as per FLT


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