On the solutions of certain Lebesgue–Ramanujan–Nagell equations
On the solutions of certain Lebesgue–Ramanujan–Nagell equations
We completely solve the Diophantine equation x2+2k11ℓ19m=yn in integers x,y≥1; k,ℓ,m≥0 and n≥3 with gcd(x,y)=1, except the case 2|k, 2∤ℓm and 5|n. We use this result to recover some earlier results in the same direction.