On the equation $f(1)1^k + f(2)2^k + ... + f(x)x^k + R(x)= by^z$

DOI10.4064/aa-51-4-349-368zbMath0661.10026OpenAlexW1017496444MaRDI QIDQ3809868

Jerzy Urbanowicz

Publication date: 1988

Published in: Acta Arithmetica (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/206179

zbMATH Keywords

congruencesgeneralized Bernoulli numbersBernoulli polynomialsperiodic functionexponential diophantine equation

Mathematics Subject Classification ID

Congruences; primitive roots; residue systems (11A07) Exponential Diophantine equations (11D61) Fibonacci and Lucas numbers and polynomials and generalizations (11B39)

Related Items (5)

A note on the equation \(1^ k+2^ k+\cdots+(x-1)^ k=y^ m\) ⋮ On the Diophantine equation (x − d)4 + x4 + (x + d)4 = yn ⋮ Polynomial values of (alternating) power sums ⋮ A computational approach for solving $y^2=1^k+2^k+\dotsb+x^k$ ⋮ The equation $(x-d)^5+x^5+(x+d)^5=y^n$

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