Explore Diophantine Equations

Solve Diophantine equations -- polynomial equations where only integer solutions are sought. Classify the equation by type, test for solvability, find particular and general solutions, and generate solution families. Covers linear equations, Pell equations, Pythagorean triples, and general quadratic forms.

When to Use

• Finding all integer solutions to a linear equation ax + by = c
• Solving Pell's equation x^2 - Dy^2 = 1 (or = -1)
• Generating Pythagorean triples or other parametric integer families
• Proving that a given equation has no integer solutions (via modular constraints)
• Testing solvability of a general quadratic Diophantine equation
• Finding the fundamental solution from which all others are generated

Inputs

• Required: The Diophantine equation to solve (in explicit form, e.g., 3x + 5y = 17 or x^2 - 7y^2 = 1)
• Optional: Whether to find all solutions, just one particular solution, or prove non-existence
• Optional: Constraints on variable ranges (e.g., positive integers only)
• Optional: Whether to express the general solution parametrically