The discussion focuses on finding the general solution for the Diophantine equation \(\frac{x(x-1)}{y(y-1)} = \frac{1}{2}\). Participants emphasize the importance of transforming the equation into a more manageable form to identify integer solutions. The equation can be rewritten as \(2x(x-1) = y(y-1)\), facilitating the search for pairs of integers (x, y) that satisfy the condition. The conversation highlights the relevance of algebraic manipulation in solving second-degree Diophantine equations.
PREREQUISITESMathematicians, students studying number theory, and anyone interested in solving Diophantine equations.
Lolyta said:Hello!
I am trying to find the general solution of this equation, could you help me?
\dfrac{x(x-1)}{{y(y-1)}} =1/2
Thank you so much!