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Results tagged with diophantine-equations
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user 41145
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 ...
10
votes
Accepted
Sum of two consecutive squares equals difference of two consecutive cubes
There is the following sequence of positive solutions (according to Mathematica): $a_n=\frac{1}{8} \left(\left(\sqrt{6}-2\right) \left(2 \sqrt{6}+5\right)^n-\left(\sqrt{6}+2\right) \left(5-2 \sqrt{6}\ …
- 492
2
votes
1
answer
566
views
Integer points of one Mordell equation
How can I determine all integer points of the following equation
$$y^2=x^3+10546$$
I tried Magma with
IntegralPoints(EllipticCurve([0,10546]));
but got the answer that it "could not determine th …
- 492