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Results tagged with diophantine-equations
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user 140705
Diophantine equations are polynomial equations $F=0$, or systems of polynomial equations $F_1=\ldots=F_k=0$, where $F,F_1,\ldots,F_k$ are polynomials in either $\mathbb{Z}[X_1,\ldots,X_n]$ of $\mathbb{Q}[X_1,\ldots,X_n]$ of which it is asked to find solutions over $\mathbb{Z}$ or $\mathbb{Q}$. Topics: Pell equations, quadratic forms, elliptic curves, abelian varieties, hyperelliptic curves, Thue equations, normic forms, K3 surfaces ...
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Is it true that $\{x^3+2y^3+3z^3:\ x,y,z\in\mathbb Z\}=\mathbb Z$?
Above equation shown below:
$x^3+2y^3+3z^3=n$ ------------$(1)$
Above equation $(1)$ can be written as:
$ax^3+by^3+cz^3=n$
Seiji Tomita has shown that for $(a+b=c)$ there are rational solut …
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