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YCor
YCor
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Proof that x^2$x^2 + y^2 - z^2z^2$ is universal

The (ternary) quadratic form $x^2 + y^2 - z^2$ is universal, meaning that any integer $n$ can be represented as $n = x^2 + y^2 - z^2$ for some integers $x, y, z$.

My question is this: who proved this fact first? I want to know to whom I should credit this fact. The oldest literature I can find is Dickson's 1929 paper "The forms $ax^2+by^2+cz^2$ which represent all integers""The forms $ax^2+by^2+cz^2$ which represent all integers" in Bulletin of AMS (ProjectEuclid link to paper), where he gives quite a general theorem on universality of all diagonal forms. And I would think that the universality of this specific form can go back further.

Proof that x^2 + y^2 - z^2 is universal

The (ternary) quadratic form $x^2 + y^2 - z^2$ is universal, meaning that any integer $n$ can be represented as $n = x^2 + y^2 - z^2$ for some integers $x, y, z$.

My question is this: who proved this fact first? I want to know to whom I should credit this fact. The oldest literature I can find is Dickson's 1929 paper "The forms $ax^2+by^2+cz^2$ which represent all integers" in Bulletin of AMS, where he gives quite a general theorem on universality of all diagonal forms. And I would think that the universality of this specific form can go back further.

Proof that $x^2 + y^2 - z^2$ is universal

The (ternary) quadratic form $x^2 + y^2 - z^2$ is universal, meaning that any integer $n$ can be represented as $n = x^2 + y^2 - z^2$ for some integers $x, y, z$.

My question is this: who proved this fact first? I want to know to whom I should credit this fact. The oldest literature I can find is Dickson's 1929 paper "The forms $ax^2+by^2+cz^2$ which represent all integers" in Bulletin of AMS (ProjectEuclid link to paper), where he gives quite a general theorem on universality of all diagonal forms. And I would think that the universality of this specific form can go back further.

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Amir Sagiv
Amir Sagiv
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Byungchul Cha
Byungchul Cha
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Proof that x^2 + y^2 - z^2 is universal

The (ternary) quadratic form $x^2 + y^2 - z^2$ is universal, meaning that any integer $n$ can be represented as $n = x^2 + y^2 - z^2$ for some integers $x, y, z$.

My question is this: who proved this fact first? I want to know to whom I should credit this fact. The oldest literature I can find is Dickson's 1929 paper "The forms $ax^2+by^2+cz^2$ which represent all integers" in Bulletin of AMS, where he gives quite a general theorem on universality of all diagonal forms. And I would think that the universality of this specific form can go back further.