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Results tagged with diophantine-equations
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user 71090
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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A specific Diophantine equation restricted to prime values of variables.
Let $j$ be $a$, $b$, or $c$ in $x^2+x+1=(a^2+a+1)(b^2+b+1)(c^2+c+1)$. We have
$x^2+x+1 = 0\mod j^2+j+1$,
$x^2+x+1+(j-x-1)(j^2+j+1) = 0\mod j^2+j+1$,
$(x-j)(x-j^2) = 0\mod j^2+j+1$.
Since $j^2+j+1$ i …
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