Undecidability in number theory
نویسنده
چکیده
D oes the equation x + y + z = 29 have a solution in integers? Yes: (3,1,1), for instance. How about the equation x + y + z = 30? Again yes, although this was not known until 1999: the smallest solution is (−283059965,−2218888517, 2220422932). And how about x + y + z = 33? This is an unsolved problem. Of course, number theory does not end with the study of cubic equations in three variables: one might ask also about xyz − 163xyzt = 561.
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