From the blog
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Ring with p elements
Let us prove that every (unitary) ring R with p elements, p being prime, is isomorphic to ℤp. Let us consider the homomorphism φ:ℤ—>R ,…
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Can a polynomial of degree n have more than n roots?
Let’s start with some definitions. Let R be a ring and f∈R [X] a polynomial of degree n≥0, then f=a0+a1X+…+anXⁿ where a0,a1,…,an are elements of…
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Finite groups of class 2 e 3.
Let G be a finite group. We want to classify all finite groups with exactly two and three conjugacy classes. The number of conjugacy classes…
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The Diophantine equation 4X⁴-16X³+20X²-8X-3=Y²
Let’s solve the Diophantine equation: 4X⁴-16X³+20X²-8X-3=Y². Let’s suppose that X,Y are two integers satisfying the equation then: (2X²-4X-1)(2X²-4X+3)=Y². Let’s observe that 2X²-4X-1 and 2X²-4X+3 are…
Marco Damele 