We study the diophantine equation $f(u(n),y)=0$, where $f(x,y)$ is a polynomial with integral coefficients and $u:N\to Z$ is a sequence expressed as a power sum with integral bases. We completely classify the cases with infinitely many solutions. We also solve the divisibility problem of deciding when can the values of such a power sum divide infinitely often the values of another power sum.

### Diophantine equations with power sums and Universal Hilbert Sets

#### Abstract

We study the diophantine equation $f(u(n),y)=0$, where $f(x,y)$ is a polynomial with integral coefficients and $u:N\to Z$ is a sequence expressed as a power sum with integral bases. We completely classify the cases with infinitely many solutions. We also solve the divisibility problem of deciding when can the values of such a power sum divide infinitely often the values of another power sum.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11390/683276
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