Abstract
The Hilbert–Kunz multiplicity, in characteristic p, of the homogeneous co-ordinate ring of the plane curve x4+y4+z4 is known to be 3+1p2 if p≡±3(8) and 3 if p≡±1(8). We derive similar results for arbitrary irreducible trinomial plane curves, using the fact that these curves have Fermat curves as branched coverings.