On a conjecture of Pomerance

We say that k is a P-integer if the first phi(k) primes coprime to k form a reduced residue system modulo k. In 1980 Pomerance proved the finiteness of the set of P-integers and conjectured that 30 is the largest P-integer. We prove the conjecture assuming the Riemann Hypothesis. We further prove that there is no P-integer between 30 and 10^11 and none above 10^3500.Comment: 10 pages. Submitted to Acta Arithmetic

Arithmetic progressions consisting of unlike powers

In this paper we present some new results about unlike powers in arithmetic progression. We prove among other things that for given $k\geq 4$ and $L\geq 3$ there are only finitely many arithmetic progressions of the form $(x_0^{l_0},x_1^{l_1},...,x_{k-1}^{l_{k-1}})$ with $x_i\in{\Bbb Z},$ gcd$(x_0,x_1)=1$ and $2\leq l_i\leq L$ for $i=0,1,...,k-1.$ Furthermore, we show that, for L=3, the progression $(1,1,...,1)$ is the only such progression up to sign.Comment: 16 page

The spatial construction of young people's livelihoods in rural southern Africa

Young people in southern Africa, in common with young people around the world, are social agents, constructing their own lives, albeit within significant structural constraints. Unlike young people in some regions, for most the need to generate a livelihood is a key consideration. Livelihood construction is a profoundly spatial activity, yet while there have been a number of studies of the spatial construction of young people's livelihoods in African cities, the spatiality of rural livelihoods has received less attention. Rural environments pose particular challenges for livelihood construction, and require particular spatial strategies. Four are discussed here: accessing education and training; migration for work; developing extensive social networks; and producing for markets. There are, however, aspects of the spatial structuring of rural southern African societies that seriously constrain the pursuit of productive livelihoods by young people. Two are considered: migration (for reasons unconnected with young people's livelihoods) and marriage practices

Rural young people's opportunities for employment and entrepreneurship in globalised southern Africa: The limitations of targeting policies

This paper is based on a study with rural young people in Malawi and Lesotho, focusing on their possibilities for accessing (self)employment in the face of the various constraints imposed by their poor rural situations. Participatory group exercises, combined with individual interviews in two rural villages, provided personal stories about jobs and businesses that the young people were engaged in, as well as previous experiences and future plans. Constraints, as well as enabling factors, working at both individual and structural levels were analysed. Policies intended to address the needs of young people tend to seek to target the most vulnerable, often on the basis of individual-and household-level characteristics (e.g. women, orphans and AIDS-affected households). We argue that this: (1) neglects the structural factors operating at national and global levels; and (2) fails to recognise that factors interact to produce vulnerability, rather than this being rooted in separate characteristics. We demonstrate that an intersectional approach, drawn from feminist studies, is a useful theoretical lens, which, in combination with a livelihoods perspective, helps illuminate the needs of rural young people. In situations characterised by high levels of poverty and multiple vulnerabilities, we argue that it can be costly and ineffective to try to decide 'who is most vulnerable'; rather, resources can be more effectively spent in trying to improve conditions that will benefit all rural young people

Income-generating activities for young people in southern Africa: Exploring AIDS and other constraints

Copyright @ 2010 The Authors. The Geographical Journal © 2010 Royal Geographical Society (with the Institute of British Geographers). The published version of the article can be accessed via the link below.This paper reports on a study with rural young people (aged 10–24 years) in Malawi and Lesotho, focusing on their opportunities to learn skills and access capital and assets to engage in incomegenerating activities (IGAs). Participatory group exercises and individual interviews provide many examples of how young people learn skills and start small businesses, as well as an insight into their strategic thinking about engaging in these livelihood options. Various factors, including the effects of AIDS, are shown to affect young people’s prospects of succeeding in their ventures.Young people are very keen on starting IGAs, and are supported by adult members of their communities in asking for interventions to help them. We argue that expanded vocational and business training, focusing on locally appropriate types and scale of businesses, coupled with help to raise start-up capital has the potential to improve the chances of young people who are poor and/or AIDS-affected securing sustainable rural livelihoods in their futures. Since AIDS is intertwined with many other issues affecting young people’s livelihoods, it is problematic to single out and target only AIDS-affected young people with interventions on skills building and IGAs. Policymakers’ attitudes to vocational skills training and support for IGAs in Malawi and Lesotho are also explored, and policy recommendations made to support vulnerable rural young people in their attempts to build sustainable livelihoods.ESRC/DFI

Socio-economic causes of food insecurity in Malawi

The food crisis that Malawi experienced in 2002 led to hundreds – maybe thousands – of hunger-related deaths, which is more than any famine in living memory. During this famine, maize production fell by over 30% and maize prices rose by over 300% (Devereux, 2002). At the peak of the crisis, nearly a third of the population were dependent on food aid (USAID/Malawi, 2004)

On a problem of Recaman and its generalization

AbstractWe solve some cases of a conjecture of Pomerance concerning reduced residue systems modulo k consisting of the first φ(k) primes not dividing k. We cover the case when k is a prime, thus giving a complete solution to a problem of Recaman