Explicit Solutions to Small Equations

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

Chapter Chapter 1 in Polynomial Diophantine Equations, 2024, pp 1-58 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 studies Diophantine equations of the smallest size, using elementary methods, such as polynomial factorization, analysis of real solutions, analysis modulo m, methods for linear equations and equations with two monomials. It shows that these methods suffice to solve all equations of size up to 8.

Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-62949-5_1

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DOI: 10.1007/978-3-031-62949-5_1

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