Linear diophantine equations

#1

How will i solve the following equation:

14x+19y=143. it should have a solution because 14 and 19 have gcd 1 which divides 143. But it is not solvable.How???

#2

Sorry for asking at the wrong section? I did it by mistake

#3

Hello @govilayush, ok section is not a problem.
See here 14x + 19y = 143 and we know that the solution for this will always be there. So try to get one as their diff
So by some hit and trial if you just want to calculate manually,
we can see 14*(-4) + 19*3 = 1
and now we just need to multiply this whole thing with 143,
so

14*(-4) + 19*3 = 1
(14*(-4) + 19*3)*143 = 1*143
14*(-4)*(143) + 19*3*(143) = 1*143
14*(-4*143) + 19*(3*143) = 1*143
14*-572 + 19*429 = 143
so now we can say that x = -572,y = 429

I hope it is clear to you !!

#4

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