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Results tagged with diophantine-equations
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user 39770
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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Can repunits be perfect cubes?
$\frac {10^n-1} 9$ is not a cube:
Since a cube is either 0, 1 or -1 mod 9, the number of digits in the repunit is
0, 1 or -1 mod 9.
If the number of digits is -1 mod 9, you can show it's not a cube …
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