Diofant equation

In the set of integers (Z) solve the equation:

212x+316y=0212x +316y =0


Write result with integer parameter
tZt \in Z
(parameter t = ...-2,-1,0,1,2,3... if equation has infinitely many solutions)

Result

x =  -79 t
y =  53 t

Solution:

GCD(212,316)=4  xy=316212=7953=79t53t x=79t y=53t tZGCD(212,316) = 4 \ \\ \ \\ \dfrac{x}{y} = - \dfrac{ 316}{ 212} = - \dfrac{ 79}{ 53} = - \dfrac{ 79 t }{ 53 t} \ \\ x = -79t \ \\ y = 53t \ \\ t \in Z



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