Diophantine equation
Very often such problems were unresolved for centuries. With time, mathematicians  came to understand their depth (in some cases), rather than treat them as puzzles. The equation is named after Diophantus of Alexandria, a mathematician, who described them first. The restriction on integer coefficients makes sense, when one is concerned about finding Divisors, or in the case of modular arithmetic. In everyday life, many equations solve problems where only whole numbers make sense: A product is composed of many parts, but only whole pieces can be produced.