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. A Diophantine set is a subset S of Nj so that for some Diophantine equation P(x,y)=0,
n
¯
∈
S
⟺
(
∃
m
¯
∈
N
...