AbstractLet p∈{3, 23} and D∈N such that p∤D and (D, p)≠(2, 3). We prove in this paper that the diophantine equationx2+D=pz,x, z∈N has at most one solution (x, z). Moreover, we give an explicit upper bound for z
It was shown by Terjanian [12] that if p is an odd prime and x, y, z are positive integers such that...
AbstractIt is proven that the Diophantine equation x2 + 11 = 3n has as its only solution (x, n) = (4...
AbstractThe equation of the title is studied for 1 ≤ D ≤ 100. It is shown that for such values of D ...
AbstractLet p∈{3, 23} and D∈N such that p∤D and (D, p)≠(2, 3). We prove in this paper that the dioph...
summary:Let $D$ be a positive integer, and let $p$ be an odd prime with $p\nmid D$. In this paper we...
In this paper, we prove that the Ramanujan-Nagell type Diophantine equation (Dx^2+k^n=B) has at most...
In this paper, we prove that the Ramanujan-Nagell type Diophantine equation (x^2+Ak^n=B) has at most...
Recently, Yuan and Li considered a variant y2=px(Ax2-2) of Cassels\u27 equation y2=3x(x2+2). They pr...
summary:The triples $(x,y,z)=(1,z^z-1,z)$, $(x,y,z)=(z^z-1,1,z)$, where $z\in \Bbb N$, satisfy the e...
A conjecture of N. Terai states that for any integer $k>1$, the equation $x^2+(2k-1)^y =k^z$ has onl...
Let A, B be positive integers and q a prime. In this paper, we prove that the Ramanujan-Nagell type ...
summary:Consider the equation in the title in unknown integers $(x,y,k,l,n)$ with $x \ge 1$, $y >1$,...
AbstractThe equation by2 + pn = x3 is regarded as a diophantine equation in the integer variables x,...
AbstractThe title equation, where p>3 is a prime number ≢7(mod8), q is an odd prime number and x, y,...
In this paper, using a deep result on the existence of primitive divisors of Lehmer numbers due to Y...
It was shown by Terjanian [12] that if p is an odd prime and x, y, z are positive integers such that...
AbstractIt is proven that the Diophantine equation x2 + 11 = 3n has as its only solution (x, n) = (4...
AbstractThe equation of the title is studied for 1 ≤ D ≤ 100. It is shown that for such values of D ...
AbstractLet p∈{3, 23} and D∈N such that p∤D and (D, p)≠(2, 3). We prove in this paper that the dioph...
summary:Let $D$ be a positive integer, and let $p$ be an odd prime with $p\nmid D$. In this paper we...
In this paper, we prove that the Ramanujan-Nagell type Diophantine equation (Dx^2+k^n=B) has at most...
In this paper, we prove that the Ramanujan-Nagell type Diophantine equation (x^2+Ak^n=B) has at most...
Recently, Yuan and Li considered a variant y2=px(Ax2-2) of Cassels\u27 equation y2=3x(x2+2). They pr...
summary:The triples $(x,y,z)=(1,z^z-1,z)$, $(x,y,z)=(z^z-1,1,z)$, where $z\in \Bbb N$, satisfy the e...
A conjecture of N. Terai states that for any integer $k>1$, the equation $x^2+(2k-1)^y =k^z$ has onl...
Let A, B be positive integers and q a prime. In this paper, we prove that the Ramanujan-Nagell type ...
summary:Consider the equation in the title in unknown integers $(x,y,k,l,n)$ with $x \ge 1$, $y >1$,...
AbstractThe equation by2 + pn = x3 is regarded as a diophantine equation in the integer variables x,...
AbstractThe title equation, where p>3 is a prime number ≢7(mod8), q is an odd prime number and x, y,...
In this paper, using a deep result on the existence of primitive divisors of Lehmer numbers due to Y...
It was shown by Terjanian [12] that if p is an odd prime and x, y, z are positive integers such that...
AbstractIt is proven that the Diophantine equation x2 + 11 = 3n has as its only solution (x, n) = (4...
AbstractThe equation of the title is studied for 1 ≤ D ≤ 100. It is shown that for such values of D ...
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