Strong Eulerian triples

We prove that there exist infinitely many rationals a, b and c with the property that a^2-1, b^2-1, c^2-1, ab-1, ac-1 and bc-1 are all perfect squares. This provides a solution to a variant of the problem studied by Diophantus and Euler.Comment: 8 page

MIGRATIONS AND THE RIGHT TO EMPLOYMENT OF FOREIGNERS IN THE REPUBLIC OF CROATIA

There are various reasons for the migration of the population in the world, from those of war and military, political and economic, then migrations driven by natural disasters, technological development and instabilities in the labor market. Labor migrations in the EU are mostly caused by the general dissatisfaction with situation in the labor market. The Republic of Croatia has increased the annual quota for the employment of foreign workers in 2018 to 22,000. Foreigners need to know the Croatian language at the level of basic communication and they easily get a job in the Republic of Croatia. Freedom of movement of workers in the EU is regulated by the acquis communautaire and represents the legal source of primary law which regulates the access of the population to the EU labor market, which implies the provision of residence and employment of foreigners and their families, and equality of treatment towards nationals of another Member State as towards their own nationals (principle of non-discrimination). It is thought that migrants pose a threat to workers of the countries they immigrate because the mobility within the EU has increased considerably in recent years. Until now, the barriers have been mainly social, cultural and economic reasons, but as we move on, this becomes less and less a difficulty of labor force movement in the labor market. A review on the employment of foreigners in Germany will be given, and the laws of the Republic of Croatia and Germany related to this issue will be considered. The method of observation, comparative method and method of analysis and synthesis will be used in this paper

Nesigurno smještanje u Hrvatskoj: konceptualizacija više-od-prolaznih migracija na Balkanskoj ruti

The article argues that the dynamic of migration on the Balkan route is changing into something more than transit. Croatia is presented as a case in point of a site where former migration aspirations are redefined as migrants encounter various types of bordering mechanisms that decelerate migration and begin developing relations with other residents. We argue that the dynamic of mobility and immobility and the ways it entangles localities en route are crucial for understanding the changing migration patterns in the Balkans. We overview concepts such as “stuckness”, “waiting”, “permanent temporariness”, “limbo”, and “liminality”, which describe the ways in which migrants navigate between temporary and permanent states of movement and residence. Additionally, the article develops the concept of “precari¬ous emplacement” in order to move beyond transit and to capture the ambiguities between moving and staying, temporariness and permanence, and inclusion and exclusion. The concept highlights that the practices related to settling, along with the social interactions with other residents associated with them, occur in conditions of uncertainty and social marginalisation. Precarious emplacement encompasses the ways precarity permeates migrants’ experiences and the fabric of post-war and post-socialist urban spaces and relations they move through and come to inhabit. The article concludes by arguing that, given the heterogeneity of migrants’ life trajectories, the concept of a “transit migrant” may obscure the vulnerabilities migrants experience during periods of immobility, and it advocates for a more nuanced conceptual approach.U radu se raspravlja o tome da se dinamika migracija na Balkanskoj ruti mijenja u nešto više od tranzita. Hrvatska je predstavljena kao primjer mjesta gdje se nekadašnje migracijske težnje redefiniraju jer se migranti susreću s različitim mehanizmima granične kontrole koji usporavaju migraciju te počinju razvijati odnose s drugim stanovnicima. Autor tvrdi da su dinamika mobilnosti i nepokretnosti, kao i načini na koje se one isprepleću na putu, ključni za razumijevanje promjenjivih migracijskih obrazaca na Balkanu. Daje se pregled pojmova kao što su »zaglavljenost«, »čekanje«, »trajna privremenost«, »limbo« i »liminalnost«, koji opisuju načine na koje se migranti kreću između privremenog i stalnog pokreta te boravka. Dodatno, članak razvija koncept »nesigurnog smještanja« kako bi se pomaknuo dalje od tranzita i uhvatio dvosmislenosti između preseljenja i ostanka, privremenosti i trajnosti te uključivanja i isključivanja. Koncept naglašava da se prakse vezane uz naseljavanje, zajedno s društvenim interakcijama s drugim stanovnicima koji su s njima povezani, odvijaju u uvjetima neizvjesnosti i društvene marginalizacije. Nesigurno smještanje obuhvaća načine na koje nesigurnost prožima iskustva migranata te poslijeratne i postsocijalističke urbane prostore i odnose kroz koje prolaze i dolaze ih nastaniti. Članak zaključuje tvrdnjom da, s obzirom na heterogenost životnih putanja migranata, koncept »tranzitnog migranata« može prikriti ranjivosti koje migranti doživljavaju tijekom razdoblja nepokretnosti te se zalaže za nijansiraniji konceptualni pristup

Householder\u27s approximants and continued fraction expansion of quadratic irrationals

There are numerous methods for rational approximation of real numbers. Continued fraction convergent is one of them and Newton\u27s iterative method is another one. Connections between these two approximation methods were discussed by several authors. Householder\u27s methods are generalisation of Newton\u27s method. In this paper, we will show that for these methods analogous connection with continued fractions hold

Estrogen and Progesterone Receptor Status in Primary Breast Cancer – A Study of 11,273 Patients from the Year 1990 to 2002

The aim of this study was to gain insight of the breast cancer hormone receptor status of our patients, its stratification according to age as well as its changes during the period of 13 years. 11,273 patients with primary breast cancer from several towns in Croatia were included in this study. Patients’ tumour specimens were collected from 1990 to 2002 and were analysed on estrogen (ER) and progesterone (PR) receptors in the Laboratory of the Department of Medical Oncology, University Hospital Centre Zagreb. More than half of our breast cancer patients had ER positive tumours (54.3%). We observed ER+ tumours increased with age continuously, with highest percentage in the age group of 70 to 79 years (68.1%). Similarly, proportion of PR+ tumours was higher in the older age groups, being the highest between 40 and 49 years (55.9%). During 13 years of the study, the increase in frequency and proportion of ER+ tumours was observed (from 52% in 1990 to 62% in 2002) and decrease of PR+ tumours (56% to 53%). We confirm previous findings that the risk of hormone dependent breast cancer increases with aging. Risk of ER+ breast cancer increased for 10% from 1990 to 2002 and PR+ tumours decreased for 3.5% in the same period