AbstractLet k be an odd positive integer. Davenport and Lewis have shown that the equations a1x1k+…+anxnk=0 with integer coefficients, have a nontrivial solution in integers x1,…, xN provided that N⩽[36klog6k] Here it is shown that for any ϵ > 0 and k > k0(ϵ) the equations have a nontrivial solution provided that N⩽8log 2+ϵk log k
P. Knapp In 1966, Davenport and Lewis published their paper ‘Notes on congruences III’, in which the...
We give the complete solution (n, a, b, x, y) of the title equation when gcd(x,y) = 1, except for th...
AbstractIt is proved that the equation of the title has a finite number of integral solutions (x, y,...
AbstractLet k be an odd positive integer. Davenport and Lewis have shown that the equations a1x1k+…+...
AbstractIt is known that a system of two additive equations of degreekwith greater than 4kvariables ...
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/135506/1/plms0354.pd
AbstractLet Fx1,…,xs be a form of degree d with integer coefficients. How large must s be to ensure ...
AbstractEstimates are given for the number of variables required to solve p-adic equations. In parti...
AbstractIt is shown that if λ1, …, λ5 are non-zero real numbers, not all of the same sign, and at le...
AbstractA special case of a conjecture attributed to Artin states that any system of two homogeneous...
In this paper, we prove that the Ramanujan-Nagell type Diophantine equation (x^2+Ak^n=B) has at most...
AbstractDenote by k = k(N) the least integer for which there exists integers b1, b2, …, bk satisfyin...
In this work, I examine specific families of Diophantine equations and prove that they have no solut...
AbstractIf F is a form of odd degree k with real coefficients in s variables where s ≥ c1(k), then t...
For relatively prime integers $a$ and $b$ both greater than one and odd integer $c$, there are at mo...
P. Knapp In 1966, Davenport and Lewis published their paper ‘Notes on congruences III’, in which the...
We give the complete solution (n, a, b, x, y) of the title equation when gcd(x,y) = 1, except for th...
AbstractIt is proved that the equation of the title has a finite number of integral solutions (x, y,...
AbstractLet k be an odd positive integer. Davenport and Lewis have shown that the equations a1x1k+…+...
AbstractIt is known that a system of two additive equations of degreekwith greater than 4kvariables ...
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/135506/1/plms0354.pd
AbstractLet Fx1,…,xs be a form of degree d with integer coefficients. How large must s be to ensure ...
AbstractEstimates are given for the number of variables required to solve p-adic equations. In parti...
AbstractIt is shown that if λ1, …, λ5 are non-zero real numbers, not all of the same sign, and at le...
AbstractA special case of a conjecture attributed to Artin states that any system of two homogeneous...
In this paper, we prove that the Ramanujan-Nagell type Diophantine equation (x^2+Ak^n=B) has at most...
AbstractDenote by k = k(N) the least integer for which there exists integers b1, b2, …, bk satisfyin...
In this work, I examine specific families of Diophantine equations and prove that they have no solut...
AbstractIf F is a form of odd degree k with real coefficients in s variables where s ≥ c1(k), then t...
For relatively prime integers $a$ and $b$ both greater than one and odd integer $c$, there are at mo...
P. Knapp In 1966, Davenport and Lewis published their paper ‘Notes on congruences III’, in which the...
We give the complete solution (n, a, b, x, y) of the title equation when gcd(x,y) = 1, except for th...
AbstractIt is proved that the equation of the title has a finite number of integral solutions (x, y,...
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