If $(a,b)$, $(a,y)$ and $(b,x)$ = $1$, show that $(ab, ax + by)$ = $1$
I tried to do this by showing that $(a,by)$=$1$ and $(b,ax)$=$1$. But then I got completely stuck. I tried to use Bezout's theorem, but ended up with nothing.
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SANTANU NANDI
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