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South African Mathematics Olympiad Second Round

Algebra Difficulty 3.8 AMC 10/12 Find the answer South Africa

If the product of four consecutive integers is equal to the value of one of those integers, then what is the largest possible value for any of the integers?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

With a little trial and error it should soon be clear that this scenario is only possible if one of the integers is zero. The options are $-3$ ; $-2$ ; $-1$ ; $0$ or $-2$ ; $-1$ ; $0$ ; $1$ or $-1$ ; $0$ ; $1$ ; $2$ or $0$ ; $1$ ; $2$ ; $3$ . The largest possible integer is thus $3$ .

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Source: MathNet, licensed CC-BY-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.