 The tenth on Hilbert’s famous list of important open problem in mathematics from 1900 asks for a decision method for the so-called Diophantine equations. Despite the unfamiliar term “Diophantine,” what is at issue here is truly elementary. Consider any equation with one or more variables and with integer coefficients, which involves only addition and multiplication, such as \(x^2 + y^2 = 2\), or \(3x^2 + 5y^2 + 2xy = 0\). If real-number solutions are sought, one usually speaks simply about an “equation”. However, in number theory, typically a solution is sought consisting only of integers. That makes a great difference. The former of the above equations has infinitely many solutions among real numbers, but only four among integers. The equation \(x^2 + y^2 = 3\) also has infinitely many real solutions but no integer solutions. When the focus is on the integer solutions, one talks about “Diophantine equations” (after the ancient number theorist Diophantus of Alexandria). 