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Abstract. A famous problem posed by Diophantus was to find sets of distinct positive rational numbers such that the product of any two is one less than a rational square. Some sets of six such numbers are presented and the computational algorithm used to find them is described. A classification of quadruples and quintuples with examples and statistics is also given.

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The construction of the KAT-7 array in the Karoo region of the Northern Cape in South Africa was intended primarily as an engineering prototype for technologies and techniques applicable to the MeerKAT telescope. This paper looks at the main engineering and scientific highlights from this effort, and discusses their applicability to both MeerKAT and other next-generation radio telescopes. In particular we found that the composite dish surface works well, but it becomes complicated to fabricate for a dish lacking circular symmetry; the Stirling cycle cryogenic system with ion pump to achieve vacuum works but demands much higher maintenance than an equivalent Gifford-McMahon cycle system; the ROACH (Reconfigurable Open Architecture Computing Hardware)-based correlator with SPEAD (Streaming Protocol for Exchanging Astronomical Data) protocol data transfer works very well and KATCP (Karoo Array Telescope Control Protocol) control protocol has proven very flexible and convenient. KAT-7 has also been used for scientific observations where it has a niche in mapping low surface-brightness continuum sources, some extended HI halos and OH masers in star-forming regions. It can also be used to monitor continuum source variability, observe pulsars, and make VLBI observations.