On Sharipov's counterexample to Khabibullin's conjecture

TL;DR

This paper examines Sharipov's counterexample to Khabibullin's conjecture, demonstrating its implications across all three equivalent statements of the conjecture.

Contribution

It transfers Sharipov's counterexample to the other two statements, showing the conjecture's invalidity in all forms.

Findings

Counterexample invalidates all three statements of the conjecture

Sharipov's counterexample applies to multiple equivalent formulations

The conjecture is disproven in its current form

Abstract

Khabibullin's conjecture has three statements equivalent to each other. Recently Ruslan Sharipov has constructed a counterexample to this conjecture for one of its three statements. In this paper Sharipov's counterexample is transferred to the other two statements of Khabibullin's conjecture.