Let p be a prime. A set A of residues modulo p is said to be sum-free if there are no solutions to a = a′ + a″ with a, a′, a″ ∈ A. We show that there are 2p/3+o(p) such sets. We also count the number of distinct sets of the form B + B, where B is a set of residues modulo p. Once again, there are 2p/3+o(p) such sets.
Authors:I. F. Édes, Z. Ruzsa, T. Szűk, Gy. Szabó and B. Merkely
Rotational atherectomy (RA) is an advanced coronary debulking technique, often used in cases, where traditional percutaneous coronary intervention (PCI) methods (e.g. balloon predilatation, use of cutting balloons, direct stenting etc.) are inadequate. We report a case of a male patient, who previously underwent PCI of the right coronary artery (RCA) and was free of chest pain for several weeks, but his clinical symptoms have developed again. Angiography showed a “de novo”, highly calcified left anterior descending (LAD) lesion that, after high-pressure balloon inflation, failed to dilate, thus the intervention was suspended. RA was scheduled for the patient within one month. As a complication of the previous LAD dilatation attempt, a chronic dissection of the target lesion occurred. Problems arose during the direct wiring attempt of the main vessel and the true lumen was only found via plaque modification, after accessing a small septal branch. Accessing the true lumen was only possible by using a conventional cross-wire. This was exchanged to a RA wire, with the help of an over-the-wire (OTW) balloon catheter. RA and debulking of the target lesion was performed. An everolimus-eluting stent (BioMatrix, Biosensors Europe, Morges, Switzerland) was implanted, with excellent results. The patient is free of clinical symptoms since the intervention, which took place 14 months ago.