Enter the coefficients A and B, along with the constant term C, into the calculator to find a solution to the Diophantine equation Ax + By = C. The calculator will provide one possible solution (x, y) if it exists.
Diophantine Equation Formula
The Diophantine equation is an equation of the form:
Ax + By = C
Where:
- A and B are coefficients of the variables x and y, respectively
- C is the constant term
- x and y are variables that take integer values
To solve the Diophantine equation, one must find integer solutions for x and y that satisfy the equation. This is typically done using the Extended Euclidean Algorithm to find the greatest common divisor (gcd) of A and B and then determining if C is divisible by the gcd. If it is, the equation has integer solutions.
How to Calculate a Diophantine Equation?
The following steps outline how to calculate a solution to the Diophantine equation:
- First, determine the coefficients A and B, and the constant term C.
- Use the Extended Euclidean Algorithm to find the gcd of A and B, and the coefficients x and y that satisfy Ax + By = gcd(A, B).
- Check if C is divisible by the gcd. If it is not, there is no integer solution.
- If C is divisible by the gcd, multiply the coefficients x and y found in step 2 by C/gcd to find an initial solution to the equation.
- Use the calculator above to verify your solution or to find a solution if you have the values for A, B, and C.
Example Problem:
Use the following values as an example problem to test your knowledge:
A (Coefficient of x) = 15
B (Coefficient of y) = 25
C (Constant term) = 100
