Quadratic Congruence Solver

Unlock solutions to equations of the form $ax^2 + bx + c \equiv 0 \pmod{m}$ . Visualize results and deepen your understanding of modular arithmetic.

Equation Inputs

Coefficient

$$a$$

Coefficient

$$b$$

Constant

$$c$$

Modulus

$$m$$

Actions

Solutions:

Visualization

Explore the graph of $ax^2 + bx + c \pmod{m}$ . Solutions are the x-intercepts. Interact with the plot to zoom and pan.

Understanding Quadratic Congruence

A quadratic congruence is a congruence relation of the form $ax^2 + bx + c \equiv 0 \pmod{m}$ , where a, b, and c are integers, and we seek to find integer solutions for x. This tool helps you solve these congruences by testing all possible values of x modulo m and visualizing the results. The solutions are the values of x for which $$$ax^2 + bx + c$$$ is divisible by m. This concept is fundamental in number theory and modular arithmetic, with applications in cryptography and computer science. For further learning, explore resources on modular arithmetic and congruence relations.