Abstract: Unless otherwise stated, we’ll work with the natural numbers: $$N = \{0,1,2,3, \dots\}.$$ Consider a Diophantine equation F(a1,a2,...,a n ,x1,x2,...,x m ) = 0 with parameters a1,a2,...,a n and unknowns x1,x2,...,x m For such a given equation, it is usual to ask: For which values of the parameters does the equation have a solution in the unknowns? In other words, find the set: $$ \{<a_1,\ldots,a_n> \mid \exists x_1,\ldots,x_m [F(a_1,\ldots,x_1,\ldots)=0] \}$$ Inverting this, we think of the equation F = 0 furnishing a definition of this set, and we distinguish three classes:
Publication Year: 2009
Publication Date: 2009-01-01
Language: en
Type: book-chapter
Indexed In: ['crossref']
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Cited By Count: 1
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