Ramanujan, the taxicab problem for polynomials, and the abc-conjecture

Key Points

• The aim is to explore the solvability of specific polynomial equations inspired by the taxicab problem.
• Analyzed the famous taxicab problem as a foundation for new equations.
• Investigated solvability for equations of the form p^n + q^n = r^n + s^n.
• Extended analysis to the general case with polynomials in multiple variables.
• Confirmed relationships between certain polynomial equations and the taxicab problem.
• Identified patterns that suggest deeper connections with the abc-conjecture.