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How do you find all the answers to this Diophantus equation (only whole numbers): $462x + 273y = 63$ ?

I started with finding the gcd using the Euclidean Algorithm.
$\gcd(462;273)$
$462=1*273+189$
$273=1*189+84$
$189=2*84+21$
$84=4*21+0$
$\gcd(462;273)=21$

But how do I continue? I know that you can solve it because you can divide 63 by our gcd 21.

Moo
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Peter
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    Any textbook on elementary number theory has a general formula for this type of problem. – Sam Sep 20 '22 at 08:59
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    Now extend your computation to the extended Euclidean algorithm in one of its versions, this finds numbers $u,v$ with $462u+273v=21$, the conclusion from that should be trivial. – Lutz Lehmann Sep 20 '22 at 09:24
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    You found out that gcd , so divide the equation by this gcd. If there is a solution, then the resulting equation must contain again only integer coefficients. here it is the more handy equivalent equation $$22x+13y=3$$ with the special solution $(9/-15)$. The rest should be easy. – Peter Sep 20 '22 at 09:54
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    @Peter Peter answers Peter! – Dietrich Burde Sep 20 '22 at 13:19

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