Quicmath also used to plot the graphs using the given equation. The LDE calculator is right below, and if you want to recall what linear diophantine equations are, you can find the theory after the calculator. It also has commands for splitting fractions into partial fractions, combining several fractions into one and cancelling common factors within a fraction. This calculator solves linear diophantine equations (LDE). Using this you can expand, factor or simplify virtually any algebraic expression you choose. Quickmath-Equation Solver QuickMath is the online equation solver. This too also able to solve an inequality, whether it is a first-degree inequality or inequality of the second degree, again the solution is calculated with its exact form. Solumaths-Equation Solver Solumaths online maths software allows fraction calculation with fraction calculator, literal calculus, numerical computation, calculation on radicals, calculation of complex numbers with its complex numbers calculator, it has powerful features allowing it to solve an equation, equation solver allows including solve an equation, solve a quadratic equation by giving the solution in exact form.
This tool also available as mobile applications in Android and iOS platform. Symbolab offers a wealth of smart calculators including equations, simultaneous equations, inequalities, integrals, derivatives, limits, tangent line, trigonometric equations, functions and more. It provides automated step by step solutions to algebraic, trigonometric and calculus topics covering from middle school through college. It allows users to learn, practice and discover math topics using mathematical symbols and scientific notations as well as text. Symbolab-Equation Solver Symbolab is an advanced math education tool. It contains the solutions for over 60 topics within math, chemistry and physics. Where k is integer, are the solutions of Linear Diophantine equation.Wolframalpha is an advanced equation solver for Arithmetic, Algebra, Geometry, Statistics, Differential Equations, Calculus, Discrete Mathematics, Linear Algebra, Chemistry, and Physics Formulas. If we know one of the solutions, we can find their general form.īy adding to and subtracting from, we get: If either a or b is negative, we can solve the equation using its modulus, then change the sign accordingly. If c is a multiple of g, the Diophantine equation has solution, otherwise, there is no solution. If a and b are positive integers, we can find their GCD g using Extended Euclidean algorithm, along with и, so: To find the solution one can use Extended Euclidean algorithm (except for a = b = 0 where either there is an unlimited number of solutions or none).
Moreover, if (x, y) is a solution, then the other solutions have the form (x + kv, y - ku), where k is an arbitrary integer, and u and v are the quotients of a and b (respectively) by the greatest common divisor of a and b.
The following theorem completely describes the solutions: This Diophantine equation has a solution (where x and y are integers) if and only if c is a multiple of the greatest common divisor of a and b. Where a, b and c are given integers, x, y - unknowns. The simplest linear Diophantine equation takes the form: A linear Diophantine equation is an equation between two sums of monomials of degree zero or one. In mathematics, a Diophantine equation is a polynomial equation in two or more unknowns such that only the integer solutions are searched or studied (an integer solution is a solution such that all the unknowns take integer values). Since this is all about math, I copy some content from wikipedia for a start.