From the blog
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The Diophantine equation x²-y³=7.
We will prove there are not integer solution to this equation. Suppose that (x,y) is a possible solution of the Diophantine equation. If y is…
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If m is odd and n a natural number (2ᵐ-1,2ⁿ+1)=1.
In the following i denote with (a,b) the greatest common divisor between two integers a and b. Let p now be a possible prime divisor…
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There is no group G such that G’=D2n, for n≥3.
Let G be a group. We denote with G’ the commutator subgroup of G and with D2n the diedral group of order 2n, with n…
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If R is a local ring then R[[x]] is local.
Recall that if S is a commutative ring with unit, S is local if and only the set of non unit of S is an…
Marco Damele 