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Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions

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2 answers
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Why does this system of gcd equations have no solutions?

In February 2024 the following question was posed by user @Aig on Math.StackExchange: Find the solutions to the system of equations $$\begin{cases} a + b = \gcd(a^3,b^3) \\ b+c = \gcd(b^3,c^3) \\ c+a …
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