pp-adic valuation of harmonic sums and their connections with Wolstenholme primes

We explore a conjecture posed by Eswarathasan and Levine on the distribution of $p$-adic valuations of harmonic numbers $H(n)=1+1/2+\cdots+1/n$ that states that the set $J_p$ of the positive integers $n$ such that $p$ divides the numerator of $H(n)$ is finite. We proved two results, using a modular-arithmetic approach, one for non-Wolstenholme primes and the other for Wolstenholme primes, on an anomalous asymptotic behaviour of the $p$-adic valuation of $H(p^mn)$ when the $p$-adic valuation of $H(n)$ equals exactly 3

SDHx and Non-Chromaffin Tumors: A Mediastinal Germ Cell Tumor Occurring in a Young Man with Germline SDHB Mutation

Background: Mutations in genes encoding one of the subunits of succinate dehydrogenase (SDH) are involved in pheochromocytoma (PHEO) and paraganglioma (PGL) development. Over the last few years, such mutations have also been associated with non-chromaffin tumors. However, immunohistochemistry (IHC) on the tumor tissue and a study on the loss of heterozygosity (LOH) aimed at demonstrating the pathogenic role of SDHx genes have only been employed in a few cases. Case report: We describe the case of a 19-year-old Caucasian man with a germline SDHB mutation, who presented with acne vulgaris resistant to medical treatment. His follow-up for chromaffin tumors was negative, while hormonal tests revealed suppressed gonadotropins with testosterone in the upper range of normality and elevated β-human chorionic gonadotropin (β-hCG). At the whole-body enhanced CT scan, a mediastinal lesion suggestive of a germ cell tumor (GCT) was detected. 18FDG-PET (fluorodeoxyglucose-positron emission tomography) imaging showed low glucose metabolism at the mediastinal site. Surgical removal of the mass was uneventful. Pathology confirmed the diagnosis of GCT consisting of cystic teratoma (95%) and seminoma (5%). IHC for SDHB showed normal protein expression, and genetic analysis of the tumor tissue revealed the absence of SDHB LOH. Normalization of the hormonal tests and acne attenuation were achieved after surgery. Conclusion: We report an incidental association of a germinal SDHB mutation and mediastinal GCT in a young Caucasian man. Our paper highlights the importance of IHC and genetic analysis in confirming the etiologic role of SDHx genes in nonchromaffin tumors, thus excluding incidental associations