On the diophantine equation x4−q4=pynx4−q4=pyn

Let n,p and qq be odd primes. In this paper, using some arithmetical properties of Lucas numbers, we prove that if n>3n>3 and p≡3(mod4), then the equation x4−q4=pynx4−q4=pyn has no positive integer solution (x,y) satisfying gcd (x,y)=1 and 2∤y2∤y.