RU-SPB 2013 Problem 7

Let $a_1,a_2$ - two naturals, and $1<b_1<a_1,1<b_2<a_2$ and $b_1|a_1,b_2|a_2$ . Prove that $a_1b_1+a_2b_2-1$ is not divided by $a_1a_2$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.