How can light have momentum as it does not have mass and p=mv

The theory of Special Relativity, proved in 1905 (or rather the 2nd paper of that year on the subject) gives an equation for the relativistic energy of a particle;

E2=(m0c2)2+p2c2

where m0 is the rest mass of the particle (0 in the case of a photon). Hence this reduces to E=pc. Einstein also introduced the concept of relativistic mass (and the related mass-energy equivalence) in the same paper; we can then write

mc2=pc

where m is the relativistic mass here, hence

m=p/c

In other words, a photon does have relativistic mass proportional to its momentum.