 Diophantine set

In mathematics, a Diophantine equation is an equation of the form "P"("x"1, ..., "x""j", "y"1, ..., "y""k") = 0 (usually abbreviated "P"(', ') = 0) where "P"(', ') is a polynomial with integer coefficients.A Diophantine set is a subset "S" of Nj  so that for some Diophantine equation "P"(', ') = 0,

That is, a parameter value is in the Diophantine set S if and only if the associated Diophantine equation is satisfiable under that parameter value.