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Notes on diophantine equations
1953Verschiedene Bemerkungen und Parameterlösungen zu den Diophantischen Gleichungen \[ x^2+ y^2 + z^2 = 1, \quad A(x^2+ y^2 + z^2) = B(xy + x z + yz), \] und \[ (r^4 + s^4) x^4 - y^4 = z^2 \quad\text{und}\quad (r^4 - s^4) x^4 + y^4 = z^2. \]
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Exponential diophantine equations
Let \(\mathbb G\) be a commutative algebraic group over \(\mathbb C\), not containing any algebraic subgroup isomorphic to the additive group \(\mathbb G_ a\). Let \(\Gamma\) be a subgroup of \(\mathbb G(\mathbb C)\) of finite rank, that is, there is a finitely generated subgroup \(\Gamma'\) of \(\Gamma\) such that all elements of \(\Gamma/\Gamma ...openaire +2 more sources
The general relativistic constraint equations
Living Reviews in Relativity, 2021Alessandro Carlotto
exaly