Ключевые слова
Diophantine equations, integer geometry, visual approach, Pell equation, integer solutions, Heron triangles, pentagonal numbers, lattice points.
Аннотация
This article analyzes Diophantine equations from the perspective of integer geometry and highlights the scientific and pedagogical significance of a visual approach in studying them. While traditional algebraic methods are effective in determining the existence of solutions and their structure, in many cases they limit the ability to intuitively understand the internal structure of the solutions. In particular, the Pell equation is analyzed using visual approaches.