SummaryFor every t there is an explicitly given number k0 such that the equation 1k + 2k + + (x − 1)k= xk has no integer solutions x≥2 for all k0 for which the denominator of the kth Bernoulli number Bkhas at most t distinct prime factors
AbstractGiven a positive integer l, this paper establishes the existence of constants η > 1 and δ > ...
AbstractIt is proved that the equation of the title has a finite number of integral solutions (x, y,...
AbstractThe equation y2 ≡ x(x + a1)(x + a2) … (x + ar) (mod p), where a1, a2, …, ar are integers is ...
SummaryFor every t there is an explicitly given number k0 such that the equation 1k + 2k + + (x − 1)...
summary:A classical result in number theory is Dirichlet's theorem on the density of primes in an ar...
AbstractLet θ(k, p) be the least s such that the congruence x1k + … + xsk ≡ 0(mod p) has a nontrivia...
AbstractWe prove by the theory of algebraic numbers a result (Theorem 3) which, together with our ea...
AbstractLet k ≥ 4 be an integer. We find all integers of the form byl where l ≥ 2 and the greatest p...
We show that for some $k\le 3570$ and all $k$ with $442720643463713815200|k$, the equation $\phi(n)=...
AbstractLet ν(n) denote the number of distinct prime factors of n. We show that the equation n + ν(n...
A conjecture of N. Terai states that for any integer $k>1$, the equation $x^2+(2k-1)^y =k^z$ has onl...
AbstractLet k be a positive integer and f a multiplicative function with 0 < f(p) ≤1/k for all prime...
AbstractWe prove that the equation xn + (x + a)n = y2n + (y + b)2n with a, b odd has only finitely m...
AbstractT. Skolem shows that there are at most six integer solutions to the Diophantine equation x5 ...
In the present paper we show that there exist infinitely many consecutive square-free numbers of the...
AbstractGiven a positive integer l, this paper establishes the existence of constants η > 1 and δ > ...
AbstractIt is proved that the equation of the title has a finite number of integral solutions (x, y,...
AbstractThe equation y2 ≡ x(x + a1)(x + a2) … (x + ar) (mod p), where a1, a2, …, ar are integers is ...
SummaryFor every t there is an explicitly given number k0 such that the equation 1k + 2k + + (x − 1)...
summary:A classical result in number theory is Dirichlet's theorem on the density of primes in an ar...
AbstractLet θ(k, p) be the least s such that the congruence x1k + … + xsk ≡ 0(mod p) has a nontrivia...
AbstractWe prove by the theory of algebraic numbers a result (Theorem 3) which, together with our ea...
AbstractLet k ≥ 4 be an integer. We find all integers of the form byl where l ≥ 2 and the greatest p...
We show that for some $k\le 3570$ and all $k$ with $442720643463713815200|k$, the equation $\phi(n)=...
AbstractLet ν(n) denote the number of distinct prime factors of n. We show that the equation n + ν(n...
A conjecture of N. Terai states that for any integer $k>1$, the equation $x^2+(2k-1)^y =k^z$ has onl...
AbstractLet k be a positive integer and f a multiplicative function with 0 < f(p) ≤1/k for all prime...
AbstractWe prove that the equation xn + (x + a)n = y2n + (y + b)2n with a, b odd has only finitely m...
AbstractT. Skolem shows that there are at most six integer solutions to the Diophantine equation x5 ...
In the present paper we show that there exist infinitely many consecutive square-free numbers of the...
AbstractGiven a positive integer l, this paper establishes the existence of constants η > 1 and δ > ...
AbstractIt is proved that the equation of the title has a finite number of integral solutions (x, y,...
AbstractThe equation y2 ≡ x(x + a1)(x + a2) … (x + ar) (mod p), where a1, a2, …, ar are integers is ...
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