Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 4.9 AIME Find the answer

4. It is known that there exist integers $a$ , $b$ , and $c$ such that the equation $(x-a) \cdot (x-1998) + 1 = (x+b)(x+c)$ holds for any real number $x$ . Then the value of $|2a + b + c|$ is

Your answer

A number or a short expression. Spacing and $ signs are ignored.

Solution

$4.2$

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