AbstractBy an ABC-hit, we mean a triple (a,b,c) of relatively prime positive integers such that a+b=c and rad(abc)<c. Denote by N(X) the number of ABC-hits (a,b,c) with c⩽X. In this paper we discuss lower bounds for N(X). In particular we prove that for every ϵ>0 and X large enough N(X)⩾exp((logX)1/2−ϵ)
We give a complete description of the set of triples (α, β, γ) of real numbers with the following pr...
AbstractWe present here a method which allows to derive a nontrivial lower bounds for the least comm...
Agrawal, Kayal, and Saxena recently introduced a new method of proving that an integer is prime. The...
We prove that there exist infinitely many coprime numbers $a$, $b$, $c$ with $a+b=c$ and $c>\operato...
By an $abc$ triple, we mean a triple $(a,b,c)$ of relatively prime positive integers $a,b,$ and $c$ ...
AbstractBy an ABC-hit, we mean a triple (a,b,c) of relatively prime positive integers such that a+b=...
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Under Baker's explicit abc conjecture, we completely solve a conjecture of Hickerson when a product ...
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The lirst result presented in this paper is a lower bound of Q(log n) for the computation time of co...
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We give a complete description of the set of triples (α, β, γ) of real numbers with the following pr...
AbstractWe present here a method which allows to derive a nontrivial lower bounds for the least comm...
Agrawal, Kayal, and Saxena recently introduced a new method of proving that an integer is prime. The...
We prove that there exist infinitely many coprime numbers $a$, $b$, $c$ with $a+b=c$ and $c>\operato...
By an $abc$ triple, we mean a triple $(a,b,c)$ of relatively prime positive integers $a,b,$ and $c$ ...
AbstractBy an ABC-hit, we mean a triple (a,b,c) of relatively prime positive integers such that a+b=...
We prove a lower bound of Omega(1/epsilon (m + log(d - a)) where a = [log(m) (1/4epsilon)] for the h...
Under Baker's explicit abc conjecture, we completely solve a conjecture of Hickerson when a product ...
AbstractWe show that there exists an infinite sequence of sums P:a+b=c of rational integers with lar...
We study the limit points Q' of a three-dimensional set Q which encodes the reciprocal quality of a...
AbstractA lower bound for πc(x), the number of primes of the form [nc] in [1, x], is given: πc(x) ⪢ ...
AbstractThe reciprocal square root calculation α=1/x is very common in scientific computations. Havi...
The lirst result presented in this paper is a lower bound of Q(log n) for the computation time of co...
AbstractThe ABC conjecture of Masser and Oesterlé states that if (a, b, c) are coprime integers with...
AbstractA k-hitting set in a hypergraph is a set of at most k vertices that intersects all hyperedge...
We give a complete description of the set of triples (α, β, γ) of real numbers with the following pr...
AbstractWe present here a method which allows to derive a nontrivial lower bounds for the least comm...
Agrawal, Kayal, and Saxena recently introduced a new method of proving that an integer is prime. The...
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