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# Monthly Archives: November 2013

## Additive vs multiplicative densities

It is basic fact of measure theory that there is no uniform measure on a countable set such as the set of all natural numbers. However, there are many ways to measure size of subsets of . For instance, the … Continue reading

Posted in Combinatorics
Tagged addition and multiplication, Banach density, folner sequences, natural density, Upper density
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## Primes of the form x^2+2y^2

In this post I will present a quite nice proof of the following fact from elementary number theory: Theorem 1 Let be a prime number. There are such that if and only if is a quadratic residue . Recall that … Continue reading

Posted in Classic results, Number Theory
Tagged Minkowski's theorem, polynomials, primes
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