Category:Oesterlé-Masser Conjecture

This category contains pages concerning Oesterlé-Masser Conjecture:

Let $\epsilon \in \R$ be a strictly positive real number.

Formulation 1

There exists only a finite number of triples of (strictly) positive integers $\tuple {a, b, c}$ with the conditions:

$a + b = c$

$a$, $b$ and $c$ are pairwise coprime

such that:

$c > \map \Rad {a b c}^{1 + \epsilon}$

where $\Rad$ denotes the radical of an integer.

Formulation 2

There exists a constant $K_\epsilon$ such that for all triples of (strictly) positive integers $\tuple {a, b, c}$ with the conditions:

$a + b = c$

$a$, $b$ and $c$ are pairwise coprime

such that:

$c < K_\epsilon \map \Rad {a b c}^{1 + \epsilon}$

where $\Rad$ denotes the radical of an integer.

Formulation 3

There exists only a finite number of triples of (strictly) positive integers $\tuple {a, b, c}$ with the conditions:

$a + b = c$

$a$, $b$ and $c$ are pairwise coprime

such that:

$\map q {a, b, c} > 1 + \epsilon$

where $\map q {a, b, c}$ denotes the quality of $\tuple {a, b, c}$.

Source of Name

This entry was named for Joseph Oesterlé‎ and David William Masser.