 Now we make an algorithm which simply tries all possible values for
"n", "x"1, ..., "x""k" (in, say, some simple order consistent with the increasing order of the sum of their absolute values),
and prints "n" every time "f"("n", "x"1, ..., "x""k") = 0.This algorithm will obviously run forever and will list exactly the "n"
for which "f"("n", "x"1, ..., "x""k") = 0 has a solution
in "x"1, ..., "x""k".Yuri Matiyasevich utilized a method involving Fibonacci numbers, which grow exponentially, in order to show that solutions to Diophantine equations may grow exponentially.