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math.NT2013
A Note on Quartic Equations with only Trivial Solutions
Felix Sidokhine
In our notice we propose the classification of some quartic equations with only trivial solutions by the auxiliary equations. For proving trivial solutions of the quartic equations…
math.NT2013
An algorithmic proof of Bachet's conjecture and the Lagrange-Euler method
Felix Sidokhine
The goal of this notice is to present a proof of Bachet's conjecture based exclusively on the fundamental theorem of arithmetic. The novelty of this proof consists in its introduct…
math.NT2013
A Universal Quaternary Quadratic Form over Gaussian Integers
Felix Sidokhine
In this article we show that the form represents all gaussian integers. The main tools used in this proof are Fermat's little theorem (over finite field e…