Show that if $a_1b_2 − a_2b_1 = \pm 1$, then the gcd of $(a_1 + a_2, b_1 + b_2) = 1$. I don't know how to deduce that. Can someone help me?
2026-04-06 08:47:00.1775465220
Show that if $a_1b_2 − a_2b_1 = \pm 1$, then the gcd of $(a_1 + a_2, b_1 + b_2) = 1$
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HINT:
$$b_1(a_1+a_2)-a_1(b_1+b_2)=?$$
OR
$$b_2(a_1+a_2)-a_2(b_1+b_2)=?$$