x^5 - y^2 = 4 AND GAUSSIAN INTEGERS

Author:

Albertas~ZINEVI\v{C}IUS

2010 Mathematics Subject Classification:

11D41, 11H45.

Keywords:

Diophantine equation, Gaussian integers, factorization.

Abstract:

The article offers a short exposition to a classical technique of solving Diophantine equations by solving x^5 - y^2 = 4 with the help of unique factorization in the ring of Gaussian integers \mathbb{Z}[i].

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Zine-2012

Vol. 7 (15), 2011