Quadratic congruence calculator. gcd (a,pn)=pr, 0 < r < n: r odd: no solution.
-
- Quadratic congruence calculator. p=2: 1 solution (mod 2) if n-2m=1; 2 solutions (mod 4) if n-2m=2 and A=4k+1; 2 solutions (mod 2n-m-1) if n-2m > 2 and A=8k+1. Abstract Quadratic congruences are of the form \ (x^2\equiv a\) (mod \ (n\)). Tool/solver to resolve a modular equation. Indeed, the linear congruence is an equivalent to the following linear Diophantine equation: What is this calculator for? This is a linear congruence solver made for solving equations of the form ax ≡ b (mod m) a x ≡ b (mod m), where a a, b b and m m are integers, and m m is positive. gcd (a,pn)=pr, 0 < r < n: r odd: no solution. In particular, it can find modular square roots by setting a = -1, b = 0, c = number whose root we want to find and n = modulus. A modular equation is a mathematical expression presented in the form of a congruence with at least one unknown variable. The equation 3x==75 mod 100 (== means congruence), input 3x into Variable and Coeffecient, input 100 into modulus, and input 75 into the last box. Jun 27, 2025 · A congruence of the form ax^2+bx+c=0 (mod m), (1) where a, b, and c are integers. Jun 16, 2025 · This Web application can solve equations of the form ax² + bx + c ≡ 0 (mod n) where the integer unknown x is in the range 0 ≤ x < n. com and learn formula, the quadratic formula and numerous additional algebra topics Feb 24, 2025 · This online calculator is a quadratic equation solver that will solve a second-order polynomial equation such as ax 2 + bx + c = 0 for x, where a ≠ 0, using the quadratic formula. You can type numbers or numerical expressions on the input boxes at the left. Come to Alegremath. Wolfram|Alpha brings expert-level knowledge and capabilities to the broadest possible range of people—spanning all professions and education levels. Free quadratic equation calculator - Solve quadratic equations using factoring, complete the square and the quadratic formula step-by-step Right from quadratic congruence solver, ti 83 to complex numbers, we have got all the pieces included. The Legendre and Jacobi symbols are objects developed to simplify understanding of solvability of quadratic congruences. A general quadratic congruence can be reduced to the congruence x^2=q (mod p) (2) and can be solved using excludents, although solution of the general polynomial congruence a_mx^m++a_2x^2+a_1x+a_0=0 (mod n) (3) is intractable. This widget will solve linear congruences for you. . The Gauss reciprocity law enables us to easily evaluate these symbols and thus provide us with tools to determine whether the equations Free Modulo Congruence with Variables Calculator - find whether two numbers are congruent to same module step by step Free quadratic formula calculator - step-by-step solutions to help solve equations with the quadratic formula. If it is a multiple, then the number of solutions modulo m is equal to the resulting GCD. p odd: two solutions (mod pn-m). There are several algorithms for finding all linear congruence solutions, this calculator uses an algorithm for solving linear Diophantine equations in two variables. pn divides a: n=2m+1: x ≡ 0 (mod pm+1); n=2m: x ≡ 0 (mod pm). r=2m: let x=pmX, a=p2mA. Some of them have, and some of them don’t have solutions. ciio ikxnyp ovi wgryig kek cmk ryde sbal tdjplv xvxm