Existence of Polynomial Parametrizations

Bogdan Grechuk
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Bogdan Grechuk: University of Leicester, School of Computing and Mathematical Sciences

Chapter Chapter 2 in Polynomial Diophantine Equations, 2024, pp 59-106 from Springer

Abstract: Abstract The size of a polynomial with integer coefficients is computed by replacing each coefficient by its absolute value and evaluating the resulting polynomial at 2. This chapter solves all Diophantine equations of size at most 12. The methods include reducing equations by linear substitutions, using elementary properties of matrices for solving equations, as well as using properties of Euclidean domains.

Date: 2024
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DOI: 10.1007/978-3-031-62949-5_2

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