Add to ORKGIn 2001, Stewart and Yu [1] proved that there exists effectively computable positive numbers c1 and c2 such that for all positive integers x, y and z satisfying x + y = z and (x,y,z)=1, z<exp(c1G1/3(log G)3) and (if z > 2 in addition) z<exp(p'Ga), a=c2log3G*/log2G where G is the greatest square-free factor of xyz, G * = max(G,16), logi denotes the ith iterate of the logarithmic function with log1t = log t and logit = log(logi-1t ) for i = 2,3, . . . , and p' = min(px, py, pz) with px, py and pz being the greatest prime factor of x, y and z respectively. In this paper, we will take G* = max(G, 9699690) due to technical convenience and will prove that we can take c1 and c2 as c1= exp(2.6 x 1044 ) and c2= 13.6 respectively. [1] C. L. St...
AbstractThe number defined by the title is denoted by Ψ(x, y). Let u = log xlog y and let ϱ(u) be th...
AbstractLet u > 3 and β > √e/(√e−1) be real numbers and let β0=β−√e/(√e−1). Let a and q be relativel...
AbstractSuppose the integer-counting function N of a system of generalized prime numbers satisfies N...
We prove that there exist infinitely many coprime numbers $a$, $b$, $c$ with $a+b=c$ and $c>\operato...
In this short note we confirm the relation between the generalized abc-conjecture and the p-rational...
AbstractThe ABC conjecture of Masser and Oesterlé states that if (a, b, c) are coprime integers with...
This paper is the first in a series of four devoted to the abc conjecture, the Rie-mann Hypothesis, ...
AbstractThis note is an observation that the LLL algorithm applied to prime powers can be used to fi...
Note:This thesis examines the abc-conjecture, a conjectured diophantine inequality which makes a con...
Under Baker's explicit abc conjecture, we completely solve a conjecture of Hickerson when a product ...
We state well-known abc-conjecture of Masser-Oesterlé and its explicit version, popularly known as t...
ABSTRACT. Let P (m) denote the greatest prime factor of m. For integer a> 1, M. Ram Murty and S. ...
AbstractWe show that there exists an infinite sequence of sums P:a+b=c of rational integers with lar...
Regarding Euler’s (totient) function, for an arbitrary number n > 1, there exists a k that possesses...
Weakened forms of the ABC conjecture are defined in terms of the upper k’th root functions. These we...
AbstractThe number defined by the title is denoted by Ψ(x, y). Let u = log xlog y and let ϱ(u) be th...
AbstractLet u > 3 and β > √e/(√e−1) be real numbers and let β0=β−√e/(√e−1). Let a and q be relativel...
AbstractSuppose the integer-counting function N of a system of generalized prime numbers satisfies N...
We prove that there exist infinitely many coprime numbers $a$, $b$, $c$ with $a+b=c$ and $c>\operato...
In this short note we confirm the relation between the generalized abc-conjecture and the p-rational...
AbstractThe ABC conjecture of Masser and Oesterlé states that if (a, b, c) are coprime integers with...
This paper is the first in a series of four devoted to the abc conjecture, the Rie-mann Hypothesis, ...
AbstractThis note is an observation that the LLL algorithm applied to prime powers can be used to fi...
Note:This thesis examines the abc-conjecture, a conjectured diophantine inequality which makes a con...
Under Baker's explicit abc conjecture, we completely solve a conjecture of Hickerson when a product ...
We state well-known abc-conjecture of Masser-Oesterlé and its explicit version, popularly known as t...
ABSTRACT. Let P (m) denote the greatest prime factor of m. For integer a> 1, M. Ram Murty and S. ...
AbstractWe show that there exists an infinite sequence of sums P:a+b=c of rational integers with lar...
Regarding Euler’s (totient) function, for an arbitrary number n > 1, there exists a k that possesses...
Weakened forms of the ABC conjecture are defined in terms of the upper k’th root functions. These we...
AbstractThe number defined by the title is denoted by Ψ(x, y). Let u = log xlog y and let ϱ(u) be th...
AbstractLet u > 3 and β > √e/(√e−1) be real numbers and let β0=β−√e/(√e−1). Let a and q be relativel...
AbstractSuppose the integer-counting function N of a system of generalized prime numbers satisfies N...