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Zbl 0661.10026
Urbanowicz, Jerzy
On the equation $f(1)1\sp k+f(2)2\sp k+\dots +f(x)x\sp k+R(x)=by\sp z$. (English)
[J] Acta Arith. 51, No.4, 349-368 (1988). ISSN 0065-1036; ISSN 1730-6264/e

Several nice congruences are proved in the paper for generalized Bernoulli numbers and polynomials. The main result generalizes some earlier results of Györy, Tijdeman, Voorhoeve and the reviewer by proving that the diophantine equation $$ f(1)1\sp k+f(2)2\sp k+... +f(x)x\sp k+R(x)=by\sp z $$ has only finitely many solutions in rational integers $x\ge 1$, $y,z>1$ under some conditions made on the periodic function f and k.
[B.Brindza]

MSC 2000:: *11D61 Exponential diophantine equations
11B39 Special numbers, etc.
11A07 Congruences, etc.

Keywords: Bernoulli polynomials; exponential diophantine equation; congruences; generalized Bernoulli numbers; periodic function

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