R. Laniewski

collaborators

5 papers

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…

math.GM2026

Primitive norm extraction and a signed descent for the cubic Fermat equation

R. Laniewski

We give a self-contained proof of the cubic case of Fermat's theorem through a signed form of Euler's descent, with the required extraction step proved directly in $\mathbb{Z}[\sqr…

math.GM2026

Radical defects, Wieferich primes, and the $ab c$ conjecture

R. Laniewski

For coprime $a + b = c$ , the parity class in which $a$ and $b$ are odd and $c$ is even admits an exact treatment. Triples are measured by the radical excess $E_{\varepsilon}=\log c-(1+…

math.CT2026

Intensional semantics for comparison problems in arithmetic geometry

R. Laniewski

This work proposes a semantic environment for arithmetic geometry in which passage between presentations carries an explicit weight. Morphism costs induce a Lawvere generalized dis…

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

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

Primitive norm extraction and a signed descent for the cubic Fermat equation

Radical defects, Wieferich primes, and the abc conjecture

Intensional semantics for comparison problems in arithmetic geometry

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

Radical defects, Wieferich primes, and the $ab c$ conjecture