## On the Diophantine equation $$y^p = f(x_1, x_2,\ldots, x_r)$$.(English)Zbl 1435.11065

Let $$R$$ be a subgroup of the additive group of real numbers having the least element property, $$p$$ a prime number and $$f(x_1,\ldots,x_t)$$ a polynomial of the form $$f(x_1,\ldots,x_r) = B(x_1,\ldots, x_t)^p+C(x_1,\ldots, x_t)$$, where $$B(x_1,\ldots, x_t)$$ and $$C(x_1,\ldots, x_t)$$ are polynomials with real coefficients. In this paper the solutions of the equation $$y^p = f(x_1, x_2,\ldots,x_r)$$ over $$R$$ are studied and an estimate for their size is given.

### MSC:

 11D41 Higher degree equations; Fermat’s equation 11D72 Diophantine equations in many variables

### Keywords:

higher degree Diophantine equation
Full Text:

### References:

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