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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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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