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Results tagged with ag.algebraic-geometry
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user 38744
Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
2
votes
Rational solutions of the Fermat equation $X^n+Y^n+Z^n=1$
I found a parameterized solution of $X^5+Y^5+Z^5=T^5$ with $X$ and $T$ rational and $Y$ and $Z$ complex rational:
$(k^2-4k+1)^5+(2k-2+(k^2-2k+3)i)^5+(2k-2-(k^2-2k+3)i)^5=(k^2-3)^5$
There is an almos …
- 2,811
1
vote
Rational points on the elliptic curve $y^2 = x^{3} - t^{2}z^3$
If we rewrite the equation as $y^2+t^{2}z^3 = x^3$, and let $v=tz$, then $y^2+zv^2=x^3$.
If you factorize over $Q[\sqrt{-z}]$, then $(y+v\sqrt{-z})(y-v\sqrt{-z})=x^3 $.
Let $x=(a+b\sqrt{-z})(a-b\sqrt{ …
- 2,811