Problem - 1276
If integer $a$, $b$, $c$, and $d$ satisfy $ad-bc=1$. Prove $a+b$ and $c+d$ are relatively prime.
Because $a(c+d) - c(a+b) = ad-bc=1$, therefore $(a+b)$ and $(c+d)$ are relatively prime by the conclusion of # 3864.