Competition problem — Algebra — Maths Olympiad Prep

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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. Spacing and $ signs are ignored.

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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