This nal project discusses the solutions of the Diophantine equations px+qy = z2 and p3+q2 = z2. To solve the equations px+qy = z2, two cases are introduced. When p = 2 and q = 3 the Diophantine equations px + qy = z2 have innitely many solution. To solve the equations p3 + q2 = z2, three cases are introduced, (i) no solution when p = 2, (ii) exactly two solutions when p = 3 with q primes…