A Note on the Diophantine Equation x2 + 4D = yp.
On the Diophantine Equation D1x2 + D... = 4yn.
On the generalized Ramanujan-Nagell equation
On the diophantine equation
A note on perfect powers of the form
The diophantine equation
A note on the diophantine equation
On the number of solutions of the generalized Ramanujan-Nagell equation
Upper bounds for class numbers of real quadratic fields
A note on the diophantine equation
In this note we prove that the equation , , has only finitely many positive integer solutions . Moreover, all solutions satisfy , and .
A note on primes p with
A note on Jeśmanowicz' conjecture
Lower bounds for the solutions in the second case of Fermat's equation with prime power exponents
The solvability of the diophantine equation
A note on the integer solutions ofhyperelliptic equations
A note on the diophantine equation
On the diophantine equation D₁x⁴ -D₂y² = 1
On the diophantine equation
1. Introduction. Let ℤ, ℕ, ℚ be the sets of integers, positive integers and rational numbers respectively. In [7], Ribenboim proved that the equation (1) , x,y,m,n ∈ ℕ, x > 1, n > m ≥ 1, has no solution (x,y,m,n) with 2|x and (1) has only finitely many solutions (x,y,m,n) with 2∤x. Moreover, all solutions of (1) with 2∤x satisfy max(x,m,n) < C, where C is an effectively computable constant. In this paper we completely determine all solutions of (1) as follows. Theorem. Equation (1)...
A note on the number of solutions of the generalized Ramanujan-Nagell equation
A correction to the paper "Upper bounds for class numbers of real quadratic fields" (Acta Arith. 68 (1994), 141-144)
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