Or, very simply stated, given the finite set $S$ = {$a_1, ... , a_k$}, consider the diophantine equation: $$(n-a_1)...(n-a_n)=0$$. EDIT: Then we can write S as {$ \ n \ | \ \exists x : (n-a_1)...(n-a_k)=0$ }. (Thanks David)

Or, very simply stated, given the finite set $S = \{a_1, \dots , a_k\}$, consider the diophantine equation: $$(n-a_1)\dots(n-a_k)=0.$$ EDIT: Then we can write S as $\{ \ n \ | \ \exists x : (n-a_1)\dots(n-a_k)=0\ \}$. (Thanks David)

Or, very simply stated, given the finite set $S$ = {$a_1, ... , a_n$}, consider the diophantine equation: $$(x-a_1)...(x-a_n)=0$$.

Or, very simply stated, given the finite set $S$ = {$a_1, ... , a_k$}, consider the diophantine equation: $$(n-a_1)...(n-a_n)=0$$. EDIT: Then we can write S as {$ \ n \ | \ \exists x : (n-a_1)...(n-a_k)=0$ }. (Thanks David)