Lionel Ponton

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20172022

most citedTwo trees enumerating the positive rationals

1 citations · 1 across the 5 of their papers we have counts for

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math.NT2017

The Calkin-Wilf tree of a quadratic surd

Lionel Ponton

By using the Calkin-Wilf tree, we prove the irrationality of numbers of the form $α = \frac{N + p}{q}$ where $N$ is a positive integer which is not a perfect square, $p$ is a ra…

math.NT2017

L'équation diophantienne $a x^{2} - b y^{2} = 1$

Lionel Ponton

On propose une méthode de résolution effective de l'équation diophantienne $(E_{2}) : a x^{2} - b y^{2} = 1$ où $a$ et $b$ sont des entiers naturels non nuls et premiers entre eux. Cette méthod…

math.NT2017★ 1 cited

Two trees enumerating the positive rationals

Lionel Ponton

We give two trees allowing to represent all positive rational numbers. These trees can be seen as ternary and quinary analogues of the Calkin-Wilf tree. For each of these two trees…

The Calkin-Wilf tree of a quadratic surd

L'équation diophantienne ax2−by2=1

Two trees enumerating the positive rationals

L'équation diophantienne $a x^{2} - b y^{2} = 1$