Het 3n+1-vermoeden

Op de Vakantiecursus 2013 van het Platform Wiskunde Nederland laat Benne de Weger zijn licht schijnen op het 3n+1 -vermoeden. Dit is een open probleem uit de getaltheorie dat voor het eerst geformuleerd werd door Lothar Collatz in 1937. Dit artikel laat zien dat het 3n+1 -vermoeden vertakkingen en herformuleringen heeft in uiteenlopende deelgebieden van de wiskunde

Book review: Mathematical Constants

No abstract

Products of prime powers in binary recurrence sequences : part II. The elliptic case, with an application to a mixed quadratic-exponential equation

In Part I the diophantine equation [formula] was studied, where [formula] is a linear binary recurrence sequence with positive discriminant. In this second part we extend this to negative discriminants. We use the p-adic and complex Gelfond-Baker theory to find explicit upper bounds for the solutions of the equation. We give algorithms to reduce those bounds, based on diophantine approximation techniques. Thus we have a method to solve the equation completely for arbitrary values of the parameters. We give an application to a quadratic-exponential equation

Book review: Algorithmic Number Theory

Geen samenvatting

Solution to problem 10457 [1995, 464] - A surprising family of conditinued fractions

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Elliptic binomial diophantine equations

The complete sets of solutions of the equation (n k) = (m l) are determined for the cases (k, l) = (2, 3), (2,4), (2, 6), (2, 8), (3, 4), (3, 6), (4, 6), (4, 8). In each of these cases the equation is reduced to an elliptic equation, which is solved by using linear forms in elliptic logarithms. In all but one case this is more or less routine, but in the remaining case ((k, l) = (3, 6)) we had to devise a new variant of the method

Predicting the winner of the 2008 US Presidential Elections using a Sony PlayStation 3

We have used a Sony Playstation 3 to correctly predict the outcome of the 2008 US presidential elections. In order not to influence the voters we keep our prediction secret, but commit to it by publishing its cryptographic hash on this website. The document with the correct prediction and matching hash will be revealed after the elections