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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) Zbl 0661.10026
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.
Reviewer: B.Brindza

11D61Exponential diophantine equations
11B39Fibonacci and Lucas numbers, etc.
11A07Congruences; primitive roots; residue systems
Full Text: EuDML