R. Laniewski

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math.NT2026

The quality plane of $ab c$ -triples and the decomposition into gains

R. Laniewski, K. Müller

To a coprime triple $a + b = c$ we attach two coordinates, the quality $X$ and the logarithmic mass $Y$ , whose ratio $λ$ measures the balance of the triple and lies asymptotically betw…

math.NT2026

Weak Hall's conjecture, approximation gains, and continued fractions

R. Laniewski, K. Müller

For an integer solution of $y^{2} = x^{3} + k$ with $x, y \geq 1$ and $k \neq = 0$ , the integers $x^{3}$ , $∣ k ∣$ and $y^{2}$ form a triple in which one term is the sum of the other two. When $\gcd(x,y…

The quality plane of abc-triples and the decomposition into gains

Weak Hall's conjecture, approximation gains, and continued fractions

The quality plane of $ab c$ -triples and the decomposition into gains