On the Diophantine equation \(y^p = f(x_1, x_2,\ldots, x_r)\)
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.
scientific article; zbMATH DE number 6924914