%% Solution to Diophantine Equation
% Solve the Diophantine equation, 30x + 56y = 8 for x and y.
% Find the greatest common divisor and a pair of Bézout coefficients for 30 and 56.

[g,u,v] = gcd(30,56)

% u and v satisfy the Bézout's identity, (30*u) + (56*v) = g.
%
% Rewrite Bézout's identity so that it looks more like the original equation. Do this by multiplying by 4. Use == to verify that both sides of the equation are equal.

(30*u*4) + (56*v*4) == g*4

%
% Calculate the values of x and y that solve the problem.

x = u*4
y = v*4

% Copyright 2012 The MathWorks, Inc.