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Diophantine set
Solution of some Diophantine equation
Diophantine set
In mathematics, a Diophantine equation is an equation of the form P(x1, ..., xj, y1, ..., yk) = 0 (usually abbreviated P(x, y) = 0) where P(x, y) is a polynomial with integer coefficients, where x1, ..., xj indicate parameters and y1, ..., yk indicate unknowns. A Diophantine set is a subset S of N j {\displaystyle \mathbb {N} ^{j}} , the set of all j-tuples of natural numbers, so that for some Diophantine equation P(x, y) = 0, x ¯ ∈ S ⟺ ( ∃ y ¯ ∈ N k ) ( P (...
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