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with the help of the EDSAC computer at Cambridge University; their results are tabulated in 1. Mordell's original interest in this equation centered on the case d = 3 ; in particular, he wanted to know whether there existed solutions in addition to the known triples x = y = z = 1 and x = y = 4, z = —5. For the range they considered, Miller and Woollett showed that in fact no further solutions existed. As a result of their happy decision to extend the search to other values of d, they discovered several other interesting properties of equation (1.1). Perhaps the two most striking facts were the following: (a) For d = 2, all solutions in the range (1.2) belong to the family:
Gardiner et al. (Wed,) studied this question.