Including such examples as Pell's equation, for 10  points— identify these types of equations with integer coefficients for which integer solutions are sought, named for the Greek author of the Arithmetica.
The genus theorem gives a condition under which one class of them can be solved. They are the subject of Matiyasevich's theorem, which states that no general algorithm for (*) solving them exists, thus giving a negative answer to Hilbert's tenth problem. Including such examples as Pell's equation, for 10  points— identify these types of equations with integer coefficients for which integer solutions are sought, named for the Greek author of the Arithmetica.
The genus theorem gives a condition under which one class of them can be solved.
Diophantine equations