From the blog
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Equations in algebraically closed fields.
Let K be an algebraically closed field and f∈K[X,Y] non-constant. Let us prove that f has infinitely many zeros in K x K. Let us…
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Sum of squares in finite fields
Let K be a finite field. Let us prove that every element of K is the sum of two squares. Let us distinguish two cases.…
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Fermat Last theorem on ℚ(√2)
Does Fermat’s Last Theorem hold in ℚ(√2)? No, in fact it can be shown that if n>3 then the equation Xⁿ+Yⁿ=Zⁿ has no non-trivial solutions…
Marco Damele 