Areteem: MCIII Number Theory 5.19

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MCIII Number Theory 5.19

Hello!

I need some help on this problem, I tried this:

ab-cd | ab

ab-cd | cd

And other equations like that.

What should I do now?

Thanks,

Tina Jin

Let $k=ab-cd$. Since $k$ is a factor of $a$, $b$, $c$, and $d$, we can let $a=xk$, $b=yk$, $c=zk$, and $d=wk$.

Oh! I got 1=k(xy-zw) which means k=1! Thank you!

Very good!