In this paper, we show under the abc conjecture that the Diophantine equation f(x)=u!+v! has only finitely many integer solutions (x,u,v) whenever f(X) Q[X] is a polynomial of degree at least three
AbstractLet N be sufficiently large odd integer. It is proved that the equation N=n1+n2+n3 has solut...
After the proof of Zhang about the existence of infinitely many bounded gaps between consecutive pri...
AbstractThe expressions ϕ(n)+σ(n)−3n and ϕ(n)+σ(n)−4n are unusual among linear combinations of arith...
In this paper, we show under the abc conjecture that the Diophantine equation f(x)=u!+v! has only fi...
AbstractNew lower bounds are given for the sum of degrees of simple and distinct irreducible factors...
AbstractWe prove identities of Liouville type on sums of even integer functions ranging over sets of...
AbstractLet a(k,n) be the k-th coefficient of the n-th cyclotomic polynomials. In 1987, J. Suzuki pr...
AbstractIn this paper, we study the existence of multiple positive solutions to some Hamiltonian ell...
AbstractLet fbe an absolutely continuous function on [0,1] satisfying f′∈Lp[0,1], p>1, Qn-be the set...
Abstract. Using recent results on companion matrices and some bounds for eigenvalues we get inequali...
AbstractLet γ=0.577215… be the Euler–Mascheroni constant, and let Rn=∑k=1n1k−log(n+12). We prove tha...
AbstractIn this paper we prove some new existence results of nontrivial solutions for classes of ell...
AbstractWe use the explicit formula of V. Shevelev for the best possible exponent α(m) in the error ...
Let \u3c8K be the Chebyshev function of a number field K. Let \u3c8K(1)(x) := 2b0x\u3c8K(t) dt and \...
AbstractA polynomial f of degree at most n is said to be ‘self-reciprocal’ if f(z)≡znf(1/z). In this...
AbstractLet N be sufficiently large odd integer. It is proved that the equation N=n1+n2+n3 has solut...
After the proof of Zhang about the existence of infinitely many bounded gaps between consecutive pri...
AbstractThe expressions ϕ(n)+σ(n)−3n and ϕ(n)+σ(n)−4n are unusual among linear combinations of arith...
In this paper, we show under the abc conjecture that the Diophantine equation f(x)=u!+v! has only fi...
AbstractNew lower bounds are given for the sum of degrees of simple and distinct irreducible factors...
AbstractWe prove identities of Liouville type on sums of even integer functions ranging over sets of...
AbstractLet a(k,n) be the k-th coefficient of the n-th cyclotomic polynomials. In 1987, J. Suzuki pr...
AbstractIn this paper, we study the existence of multiple positive solutions to some Hamiltonian ell...
AbstractLet fbe an absolutely continuous function on [0,1] satisfying f′∈Lp[0,1], p>1, Qn-be the set...
Abstract. Using recent results on companion matrices and some bounds for eigenvalues we get inequali...
AbstractLet γ=0.577215… be the Euler–Mascheroni constant, and let Rn=∑k=1n1k−log(n+12). We prove tha...
AbstractIn this paper we prove some new existence results of nontrivial solutions for classes of ell...
AbstractWe use the explicit formula of V. Shevelev for the best possible exponent α(m) in the error ...
Let \u3c8K be the Chebyshev function of a number field K. Let \u3c8K(1)(x) := 2b0x\u3c8K(t) dt and \...
AbstractA polynomial f of degree at most n is said to be ‘self-reciprocal’ if f(z)≡znf(1/z). In this...
AbstractLet N be sufficiently large odd integer. It is proved that the equation N=n1+n2+n3 has solut...
After the proof of Zhang about the existence of infinitely many bounded gaps between consecutive pri...
AbstractThe expressions ϕ(n)+σ(n)−3n and ϕ(n)+σ(n)−4n are unusual among linear combinations of arith...
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