Moving to a new site

Hello everyone! I am sorry to inform you, but this is the last post I am going to make on this blog... because I have moved to a different site! From now on, my blog will be hosted on my university server, and you can find it here. If you are interested in the reason …

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Proof sketch of Thue’s theorem

In this post a proof of the following theorem is going to be sketched, following the treatment in Borevich and Shafarevich's Number Theory. This sketch is by no means meant to be highly detailed and I am writing it mostly for my own purposes, so I avoid proving some things, even if they aren't that straightforward. Thue's …

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IP=PSPACE

Complexity theory is a mathematical study of algorithmic problems with regard to how cost-effective solutions they have. Most prominent are the decision problems, which are yes-no questions for which answer depends on some further input, for example, "Is $latex n$ a prime number?" is a decision problem depending on the input $latex n$. I assume that …

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Starting a new project – Solutions to exercises in Marcus’ book (+some info)

The book "Number Fields" by D. Marcus is a very well-known introductory book on algebraic number theory. Its most memorable aspect is, without a doubt, the great number of exercises it contains. They vary from short(ish) computational exercises, through various technical results used later in the book, to series of exercises aimed to establish (sometimes …

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Number of irreducible polynomials over a finite field

Warning to PROMYS students: this blog post contains major spoilers regarding problems 4 and 6 of the Open Door Problem Set. Read at your own risk. The following problem has appeared as problem P3 on the short exam #2 during PROMYS Europe 2016: Let $latex p,n\in\mathbb N$ with $latex p$ prime. How many irreducible polynomials …

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