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Program finds a general formula, which gives all integer solutions to a two variable diophantine linear equation

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Two-Variable-Diophantine-Linear-Equation-Integer-Solutions

Program finds a general formula, which gives all integer solutions to a two variable diophantine linear equation.

How to call function:

To find all integer solutions to y and x of an equation:

ay = bx + c (a,b,c are constants of type int and are coprime)

Call:

DLEITVS(a, b, c)

Returns the solution equation in form:

x = pn + q

y = rn + s

(where n can be any integer)

The program returns a 2D int array in form: {{p,q}, {r,s}}, i.e. if t is the returned array:

p = t[0][0]

q = t[0][1]

r = t[1][0]

s = t[1][1]

*If a solution does not exist, it returns an arithmetic exception

Proof/Intution behind my algorithm:

Screenshot 2023-10-27 at 23-34-25 Notes - 26-10-23 Math Formulas and Proofs pdf Screenshot 2023-10-27 at 23-35-09 Notes - 26-10-23 Math Formulas and Proofs pdf Screenshot 2023-10-27 at 23-35-20 Notes - 26-10-23 Math Formulas and Proofs pdf Screenshot 2023-10-27 at 23-35-38 Notes - 26-10-23 Math Formulas and Proofs pdf

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Program finds a general formula, which gives all integer solutions to a two variable diophantine linear equation

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