Question

Suppose that p and q are unequal primes. Prove that p|x and q|x iff pq|x for x ∈ Z. Can someone confirm if my answer is right or not? my answer: pq|x --> x = p*q*k --> x/p = q*k ∈ Z --> x/q = p*k ∈ Z

Answer 1

Suppose that pa=x and qb=x for some integers a and b.
We want to prove pq(t)=x.
We also have gcd(p,q)=1 which means for some integers g and k we have
pg+kq=1

now..
multiply both sides of pg+kq=1 by x
and use the things we suppose to show pq*integer=x


we also have to go the other way since you have an iff statement