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Results tagged with ag.algebraic-geometry
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user 38620
Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
4
votes
1
answer
578
views
Find all rational solutions of $x^2(x+1)(x^2+1)(x-1)=2(y+1)(y-1)$
Find all rational solutions of
$$x^2(x+1)(x^2+1)(x-1)=2(y+1)(y-1).$$
Clearly the following six solutions hold:
$$(x,y)=(1,1),(-1,-1),(-1,1),(1,-1),(0,1),(0,-1)$$
But how to find all rational solution …
- 4,280
2
votes
0
answers
242
views
Can estimate upper bound of $|p_{i}|$ or $|q_{i}|?$
when I Find the diophantine-equation rational points $$2y^2=x^6-x^2+2$$
I using Faltings's theorem showed that there are only finitely many solutions,if we assmue that
$(x_{i},y_{i}),i=1,2,\cdot …
- 4,280