Let c be a square-free positive integer and pa prime satisfying p\not ∣ cp∤ c. Let h (-c) h (-c)
denote the class number of the imaginary quadratic field Q (-c) Q (-c). In this paper, we …

We study the exponential Diophantine equation $ x^ 2+ p^ mq^ n= 2y^ p $ in positive
integers $ x, y, m, n $, and odd primes $ p $ and $ q $ using primitive divisors of Lehmer …

We consider the Lebesgue-Ramanujan-Nagell type equation $ x^ 2+ 5^ a13^ b17^ c= 2^
my^ n $, where $ a, b, c, m\ge 0, n\ge 3$ and $ x, y\ge 1$ are unknown integers with $\gcd …

We investigate the solvability of the Diophantine equation in the title, where d> 1 d> 1 is a
square-free integer, p, q are distinct odd primes and x, y, a, b are unknown positive integers …

Let a, b be fixed positive integers such that 2∤ ab, gcd (a, b)= 1 and a is square-free, and let
h (-a) denote the class number of the imaginary quadratic field Q (-a). Further, let n be a fixed …

We consider the Lebesgue-Ramanujan-Nagell type equation $ x^ 2+ 5^ a13^ b17^ c= 2^
my^ n $, where $ a, b, c, m\geq 0, n\geq 3$ and $ x, y\geq 1$ are unknown integers with …

We consider the Diophantine equation 7 x 2+ y 2 n= 4 z 3. We determine all solutions to this
equation for n= 2, 3, 4 and 5. We formulate a Kraus type criterion for showing that the …