OME 2005 Problem 1

Let $a$ and $b$ be integers. Demonstrate that the equation $(x-a)(x-b)(x-3) +1 = 0$ has an integer solution.

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.