On the Diophantine equation \(y^p = f(x_1, x_2,\ldots, x_r)\)
type: Item
instance of: scholarly article
title: On the Diophantine equation \(y^p = f(x_1, x_2,\ldots, x_r)\)
zbMATH Open document ID: 1435.11065
author: R. Srikanth
author: S. Subburam
published in: Functiones et Approximatio. Commentarii Mathematici
publication date: 2018-08-24T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.facm/1512183755
review text: 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.
Mathematics Subject Classification ID: 11D41
Mathematics Subject Classification ID: 11D72
zbMATH DE Number: 6924914
zbMATH Keywords: higher degree Diophantine equation
reviewed by: Dimitros Poulakis
MaRDI profile type: Publication
OpenAlex ID: W2772367098
cites work: A simple method for solving the Diophantine equation \(Y^2=X^4+aX^3+bX^2+cX+d\)
cites work: ESTIMATES FOR THE SOLUTIONS OF CERTAIN DIOPHANTINE EQUATIONS BY RUNGE'S METHOD
cites work: The diophantine equation \((y+q_1)(y+q_2) \cdots (y+q_m) = f(x)\)
cites work: Q3189241
cites work: On the Diophantine equation \(ax^3 + by + c = xyz\)
cites work: Fast algorithm for solving superelliptic equations of certain types
cites work: Q4781843
cites work: Algorithm to solve certain ternary quartic Diophantine equations
DOI: 10.7169/FACM/1635
description: scientific article; zbMATH DE number 6924914