Details

Davide Lombardo ^[a]

A family of quintic Thue equations via Skolem’s \(p\)-adic method

Pages: 161-173
Received: 5 May 2021
Accepted: 2 September 2021
Mathematics Subject Classification: 11D59, 11D88, 11D41.
Keywords: Skolem's method, \(p\)-adic methods, Thue equations, Diophantine equations.
Authors address:
[a]: Dipartimento di Matematica, Università di Pisa, Largo Bruno Pontecorvo 5, 56127 Pisa, Italy.

Abstract: We solve the diophantine equation \(m^5+(4 \cdot 5^4 b^4)m n^4 - n^5=1\) for all integers \(b \neq 0\). This gives an example of a family of quintic Thue equations that can be solved completely by using nothing more than Skolem's \(p\)-adic method. We also give a general introduction to Skolem's method from a modern perspective.

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